I couldn't find a video of it running in 2 players mode. I can't imagine this game in 2 players, it sounds insane
The 2 player mode in the C64 version is similar to the Mario games where the players switch if one of them dies. We (a friend and me) had this competition going who could go the furthest but none of us could ever beat the game, the jumping is unusual because you have to press up on the C64 Stick to jump but it has its own charm for being different. If i remember correctly then you could play 2 player mode with only one controller.
Here is a video of showing 2 player mode in the C64 version, the video itself is 1P only.https://youtu.be/tiI8C-NJTq8?t=10m39s
edit: text correction