This reminds me a hole lot of the toy where you had a red and a blue boxer, you had these buttons that made your guy punch the other guy. Honestly this is boxing nostalgia for me, loved to play that with my bro. nice game 9/10.
Rock 'em Sock 'em robots! Someone pointed that out, so I looked it up. Glad you loved it.
Source: https://www.theoldrobots.com/RockEm.html
Time for that rematch with your bro, but this time with Toe to Toe.