The game is Super Mario Bros 3 from the NES.
There is no need to explain – everyone knows Mario.
This is a good version of the game and one of the games that offers a 2 player option.
The only downside to this game is there is no password and as you can’t save you would have to complete it in one go if you wanted to see the whole game!
Unlikely for me since I can’t even beat Bowser in world 1…