OK, so here's what I learned!
There seems to be some CRITICAL bugs with K/X/Ubuntu 15.04 and Linux Mint 17.2, where for some reason the programs will compile but NOT launch. No error messages are generated or anything, there's just nothing that happens.
So, I "downgraded" to Kubuntu 14.04 LTS, ran some updates, uninstalled the AMD proprietary drivers, and what do you know, suddenly the programs work! I ran Santa's Bad Elf and it ran flawlessly, and ran my own really basic code.
I may truly never use Windows again if AppGameKit gets really popular in the Linux community!
EDIT: Another quick note.
I installed the proprietary drivers for AMD through Driver Manager and now everything works even better.
No screen tearing, no problems rendering anything in AGK. I don't know why it made a difference downloading it through the Driver Manager but somehow it did.
Forum President until June 20th, 2016. Bow down to me!