This is a good, already vegan chocolate cake. If you have a gluten-free flour mix you like, I think this cake would probably take well to it:
https://moosewoodcooks...
It's based on a Depression-era recipe and there are lots of other versions, often called something like "wacky cake" or "crazy cake." There are a few examples made with gluten free flour kicking around the internet, and it seems like they were done with a straight 1:1 replacement for wheat flour.

If he's open to chocolate dessert other than cake, there are wonderful mousses that use chocolate, avocado & sweetener. Can be garnished with any fruit he likes, or gluten-free crunchy topping.

This doesn't answer all parts of your question: I haven't made it, so I don't know how good it is. But maybe you could try this Food52 recipe for Chocolate Mochi Snack Cake (https://food52.com/recipes...) with a few substitutions. Someone in the comments successfully subbed the evaporated milk for coconut milk, and you could sub the eggs with applesauce or a flaxseed slurry. Since you want something denser than the Moosewood cake, eliminating the eggs might work to your advantage here.

Report back on what you did!

You could try subbing 1/4c silken tofu per egg. I've done it in chocolate chip cookies and cheesecake with excellent results.