An executable problem like exe does not work on Linux (without wine). When compiling source code compiler produce object code which is specific to a particular cpu architect
Problem 1 is the image format. When an application is launched into execution the Os has to load the applicaiton image, find out its entry point and launch it from there. That means that the OS must understand the image format and there are different formats between various OS.
Problem 2 is access to devices. Once launched an application can read and write registries in the CPU and that's about it. To do anything interesting, like to display a character on a console, it needs access to devices and that means it has to ask for such access from the OS. Each Os has a different API that is offered to access such devices.
Problem 3 is priviledges instructions. The newly launched process would perhaps need a memory location to store something, can't accomplish everything with regiestries. This means it needs to allocate RAM and set up the translation from VA to physical address. These are priviledges operations only the OS can do and again, the API to access these services vary between OSs.
Bottom line is that applications are not writen for a CPU, but for a set of primitive services the OS offer. the alternative is to write the apps against a set of primitive services a Virtual Machine offers, and this leads to apps that are more or less portable, like Java apps.