It’s a capacitor that’s used in conjunction with the bridge rectifier. I once bought a pair of Williams Star Pool projects from a guy who said the bridge rectifiers were bad. They weren’t, at least not the one I used (I took the best of both projects for the pin I kept and sold the rest as a project). Once I went through the machine, everything worked fine. I believe the bridge rectifier also supplies DC power to the slingshots, so if those are working, I’d guess the capacitor and bridge rectifier aren’t the problem with the pop bumpers.

Unfortunately, I bought a bridge rectifier before I realized I didn’t need a new one. Glad you found out before I did.