A couple things for clarification. First, some have speculated that the percentages do not refer to true percentages. Assuming this is UK labeling, as in the link rumtscho noted, the 96% per UK regulations must refer to the amount per 100 grams of the product by weight (from 96.2 grams of whole wheat). It turns out I was wrong about this in some cases. See NOTE added at the end of this answer. Canadian versions note that Shreddies are 94.9% "whole grain wheat."
That seemingly leaves only about 4-5% of other ingredients for sugar. As rumtscho points out, "sugar" here can include all sorts of different chemicals that count as "sugars." The ingredients list includes sugar, invert sugar syrup, barley malt extract, and molassses, all of which will contain sugars that likely contribute to the total.
And yet that still doesn't seem to be enough. I was confused at first too, as whole wheat flour only contains roughly a gram of sugars. I consulted a half dozen different products and different nutritional databases, and whole wheat flour and whole wheat berries contain around a gram of sugar per 100 grams. (It varies a bit by wheat variety, but seems to usually be in the range of 0.5-1.5 grams of sugar per 100 grams.)
So what's going on? That only seemingly accounts for maybe 5-6 grams of sugar, as OP notes. I agree that at first it was a mystery to me too. Then I went to the Shreddies website and noticed the description -- "delicious malty, milk-loving squares."
Lacking another explanation, the issue must be in the "malting." At first, one might assume the malt extract is what creates the malty flavor, but whole grains can easily be malted (that is, allowing them to sprout a bit, which also develops natural enzymes in the grain to convert carbohydrates and starches into sugars). The added barley malt, assuming it contains active enzymes, can also assist in this conversion to sugar.
As noted on this Canadian site:
Many varieties of Shreddies either use a malted cereal process or use
additions of malt extract. We could not find if Canadian manufactured
Shreddies uses Malting. If malting is used the grains would develop
enzymes through the germination process that turn the starches into
starches and sugars such as maltose through the forced germination
process of malting. The resulting rootlets would then be removed and
recycled into valuable animal feed.
The malting process provides colour and flavour to the product. There
is also a possibility that malting extract may also be used in the
flavouring of products. The malt extract is the filtered and
evaporated sweet liquid that is extracted and evaporated during the
germination process which contains mostly maltose (malt sugar) from
the malting process of barley or wheat.
Malting preserves the natural characteristics of whole grain and
extracts are nutritious and functional to processing. (Vitamin
B, and used as a substitute for refined sugar, and amino acids.)
To my mind, that's the only reasonable explanation, unless Shreddies is made from some bizarre engineered wheat variety that has oodles more sugar than usual. As that site quoted above notes: "Processing information is very difficult to discover on Shreddies." While some products will definitely advertise malting of ingredients as part of their process, I don't know what the labeling requirements in the UK are for this.
However, it's easily possible that malting of the whole-grain wheat could double the sugar content of the final cereal, as is likely the case here. Note that in this case the sugar is not "added," but instead effectively converted from the natural carbohydrates and starches in the whole wheat to sugars. (Also, it's important to note that this process will happen in your digestive system anyway when you eat whole grains, as the human body breaks down many carbohydrates into simpler sugars. I'm not saying there is no nutritional difference, only that the total number of carbohydrates you are ingesting from the whole wheat is likely about the same.)
EDIT -- IMPORTANT NOTE: After further research, I realized I'm wrong about the implications of EU labeling. The relevant information can be found at this link, but there are also UK resources that confirm this interpretation.
As discussed there, Chris H's interpretation may in fact be what's going on here too. That is, they may begin with 96 grams of whole wheat, add 13 grams of sugars (in various forms), then bake the cereal, causing water to evaporate from the wheat, and then still claim that whole wheat is 96% of the total ingredients, even with 13 grams added sugar. It sounds preposterous, but the example near the bottom of the EU regulations linked above says this is actually the way to label this process. The only time when they need to explain this absurdity is if the ingredients required to be labeled with percentages (otherwise known as a quantitative ingredient declaration, or QUID) seem to add up to more than 100%, in which case there needs to be clarification. However, since the packaging doesn't make any statements about the added sugars in the advertising, they aren't required to state the percentage of added sugars. So, if I'm reading these regulations correctly, even though added sugars might constitute 13% of the final product, they can still claim the product has 96% whole wheat. (See the example at point 27 in the EU link above,[SEE ADDITIONAL EDIT BELOW] which shows that the calculation for a QUID is generally the weight of the original ingredient divided by the final weight of the product, regardless of whether weight loss in the ingredient may have significantly changed the percentage in the final product.)
In sum, the sugar content here could be due to malting, or it could be due to a lot of added sugar that is effectively hidden in the ingredients declaration, due to loss of moisture and the bizarre EU method of percentage calculation. Or it could be partly both. I don't know that there's any way to know for certain without chemical analysis of the cereal or further processing details from the manufacturer.
FURTHER EDIT -- To address some concerns that have come up in comments on this answer and Chris H's answer, please note the link to a UK document on QUID that was provided by the commenter. (I found that link before too, but quoted the EU link as more recent. The comment claims the EU link is broken in my answer, but it still works fine for me. Nevertheless, I'm adding this for the sake of completeness and to show a UK source.) In any case, please consult page 14 in the UK link under section 43 to see the same calculation on butter cookies I mentioned above in my last edit. For the sake of completeness, I quote that regulation in detail here:
- QUID declarations on products (such as cakes, biscuits, pies and cured meats) the composition of which has been changed by cooking or other treatments involving loss of moisture should be based on the amount of the ingoing ingredient expressed as a percentage of the weight of the final product. For example, the butter content of a “butter cookie” would be calculated as follows:
List item Weight
Total mixing bowl 195g
Total after baking 169g
Formula: 50/169 x 100 = 29.6% Where this calculation would lead to declarations exceeding 100%, the declarations should be replaced with statements giving the amount of the ingredients used to make 100g/ml of the final product (eg “made with Xg/ml of Y per 100g/ml”).
In that case, the butter percentage in the butter cookies is likely overrepresented as a constituent of the final product, since the highest percentage free moisture component in the cookies was the eggs (typically ~75% water compared to ~15% water in butter and even less in flour). Nevertheless, this is the way the EU requires calculations to be done. I don't know whether this calculation method and way of adding sugar was used in OP's case or not, but the regulations appear to allow it.