If the problem you're having is that it is too watery (I assume that's what you mean by "too thin"), there might be two causes:
The recipe you linked to calls for a sizable amount of stock/broth, relative to the wine. It might be assuming that you have something closer to homemade stock, which has a high concentration of gelatin, as opposed to store-brought "broth", which is more like meat-flavoured juice.
You might not have reduced it enough. A "thin layer" could mean anything, but it's not thickness you're concerned about, it's viscosity. When the sauce has been reduced enough, it should have the consistency of... sauce. As in thick, sticky, and slow-moving. If it still looks and pours like water, it's not reduced enough.
On the subject of taste, there's also the question of which wine you use. The wine sauce is going to taste like the wine (stronger, actually), which is one of the reasons why chefs will tell you not to cook with any wine that you wouldn't drink.
It's pretty easy to make a reduction - just continue to let water boil off until it turns into the consistency you want. If you overdo it, you can always add a little extra wine to compensate.
As noted in the comment clarification - if you're simmering at a reasonable temperature, expect to wait at least an hour, and for no less than half the water to evaporate.