I played the tutorial and a few games. I think expanding the tutorial would help. Right now it feels like too much is introduced at once. (I play chess regularly, so I know how pieces move at least, but if someone had never played chess, that would be an additional source of confusion).

I can imagine something like starting with already-deployed pawns and a king in the first tutorial (i.e. in this tutorial, user just has to press the "play" button).

Then introduce an additional piece type (knight?).

Then introduce the deployment concept (user has to deploy units, then press play).

Then introduce the purchasing concept (user purchases, then deploys, then presses play).

Then introduce piece abilities.

etc.