Yes, there are two schools of marshmallow thought - with egg whites and without egg whites. Most recipes without egg whites have another difference that might better explain why your recipe acts so differently from what you see with commercial marshmallows. Egg white recipes use corn syrup as only a fraction of the weight of the sugar in the recipe - recipes without egg white use a LOT of corn syrup.
A cup of sugar weighs about 7 oz. A cup of corn syrup weighs about 11 1/2 oz.
In your Epicurious recipe with egg whites, you would have about 14 oz. sugar and about 5 1/4 oz. corn syrup - so the corn syrup to sugar ratio would be somewhere between 1/3 and 1/2 - you have a fraction of your sugar weight in corn syrup.
If you look at various recipes without egg whites (Alton Brown, Joy of Baking, etc.) what you will see is the inclusion of corn syrup in almost equal weight to the sugar.
I make this point because a glance at the list of ingredients on a package of commercial marshmallows will show corn syrup as the first ingredient - that means that there is more of that ingredient, by weight, than any other ingredient.
I have only made marshmallows one time - without egg whites - and while they didn't behave exactly like commercial marshmallows, they were pretty similar and a LOT better.