Author here: Elo is commonly used and most gamers understand it. It's nice to be able to show each player their Elo.

I love the idea to use per-player embedding and to add a nonlinear model on top. I think it may improve the model dramatically, but I'm afraid that the model may be overfitting strongly as we have only 35 games in the historical for now. Anyway - I think I'll try this out.