Developing with AppGameKit on Linux will give you an executable file which runs on another Linux PC, provided the necessary system files are present (see
AGK documentation). That's standard and I do this flawlessly on a vanilla install of Ubuntu 16.04 (64-bit) running on a basic laptop. AppGameKit downloaded from Steam.
This may also help:
Link to article
The program you make consists of a binary (equivalent to a Windows .EXE) and some asset files in the 'Media' folder (e.g: sound files, fonts and graphics).
In theory, this can run on a "server", as that can be anything from a Raspberry Pi, to a home PC, to a blade in a server farm. If you are the "owner" or system admin on that server, you're in control. You already have the necessary skills and access.
However, you are not the owner if you just rent space with a hosting plan! I'd guess that hosted plans will be far trickier to work with - You'd need to discuss it directly with the specific host.
Your main topic will be privileges and network access!
It's up to you how your unique program functions online, via the code you write. I haven't used any networking features in my own projects, so my knowledge ends right there.
Best of luck. Feel free to share what you find out, it would be useful to know!
(Also "welcome"!)
AGK Linux user.
Tessellatus - a game of chance for Android.