Hi. There are gluten-free beers, but they're fairly carby. A lot of the alcohol will cook off, but the carbs will not.

There are LC options for thickening without flour. The simplest is just to cook it down, but that usually requires some babysitting. You could also use xanthan gum, guar gum, a product like Thickenthin Notstarch, heavy cream, tomato paste, or pureed cauliflower. I try to use a combination. If you don't care about the carbs, you can go with potato starch or corn starch.

I couldn't see the recipe because it's behind a paywall, but the beer probably acts as an acidic tenderizer. You could use a splash of dry wine instead.