I’ll comment my solution here in case anyone comes across this with a similar problem.

I installed Antimicro, it comes up under slightly different names like AntimicroX but they should all be the same.

I mapped buttons on the controller to the keyboard and it all worked. You just need to map the matching controls in the game to the controller keybinds.

This was perfect for my use case because I bought my boys these controllers:

(They’re 2 years old so I don’t want to get them good ones.)

These controllers have a few problems with them. First is games and retroarch don’t seem to recognise the D-pad inputs like normal, and second is Midtown Madness 2 defaults to a joystick axis for steering and you can’t remap this.

Antimicro has fixed these problems by mapping everything to the keyboard, allowed me to play Burnout: Paradise with a controller, and fixed the new problem of trying to play Midtown Madness 2 without analogue sticks.

Antimicro is free and open source for Windows and Linux so it should sort you out on whatever platform you’re on. I made my own profile, but you can download existing profiles from the internet as well.

Since this is an old laptop for my kids I don’t want to put Steam on there. I found a program called antimicro that translates controller inputs to keyboard keys so I’m going to try that out