Hey everyone. I spent the last couple of days trying to figure out controller remapping for steam games which didn't have support for the 8 way joysticks. I thought it was impossible until I stumbled upon the remapping within steam itself! I specifically got both polycade player one and two working with hotshot racing.
Sounds like you got player one to work... but to start, make sure you have "steam input" enabled in steam settings. Then in your library, select the game you want to modify controls for. On the right of the screen, there should be an xbox controller icon and a statement similar to, "this game partially works with your controller..." Select the link to modify controller input. You should be brought to a screen where you can select the controller you want to modify. At the top, there should be TWO links to xbox controllers. These are player one and player two separately. You have to modify each of them individually to make them work. I simply selected the xbox D-Pad icon and remapped it to the left joystick. For hotshot racing, this was all I needed to do. I saved my custom mapping and then I loaded it into controller two.
So far this system has been working great for a number of games. I even got Minecraft Dungeons working!! That one was a bit tricky, but I even got the inventory and map working along with movement with the joystick, albeit the character can only move in 8 directions, but the map designs are designed with diagonals anyways. I'm thankful for the steam input mapping. I hope this helps!! I'm happy to make screen shots if you still want to troubleshoot hotshot racing.