dnovraD: How much would it hurt you to play a source port?
https://deat.tk/jazz2/
To avoid any misinformation: This is a remake/re-imagination project and very much not a source port. The reason it doesn't qualify is because the code is completely rewritten from the ground up that has no resemblance of the oriignal games inner workings and source code. It may look somewhat the same from imported graphics, but physics and handling of this fangame is quite different than the original game, the author even says it's not his ambition to recreate a 1:1 port. Not to say you still might enjoy it though as it runs smoothly on many systems.
Anyway back on topic, I suggest looking carefully if you have all the game files, like .j2l , j2t, j2e, j2b files. I think what may be happening here is you have a controller plugged in the game isn't recognizing. Whenever you launch it goes through the menu options at lightning speed, potentionally hitting exit game straight away. Anyway, if you have a video of the issue it may be easier to help forward. Also check your jj2 installation settings to find the community add-on JJ2+, this may help fix some weird bugs. Visit website gog.jj2.plus for detailed instructions.