Actually no, an .exe can only work on windows. Linux and Mac have different formats for an executable.
I guess you got confused because of the unity export menu, it's written Windows, mac and linux but you also have a drop down menu where you select the OS. You need to make a separate build for each operating system.
That sucks ofc, I got to instal the diffrent OS to the unity version. Since I can't and won't be updating the game file on itch.io can I will create custom private link for the page with linux/mac download. Linux and Mac version : https://bordexthedev.itch.io/pump-it-up-linuxmac
Again sorry for the problems and taking up your time. Hope you enjoy the game (: