I’m pretty sure that you can’t externally mod/control an Xbox 360 with a Macintosh.
Generally speaking people physically mod the Xbox 360 and then run mod on it.
There is a plethora of information on how to do so in this site.
As far as gaming goes Macintosh is well know for supporting any major titles.
I once bought GTA San Andreas for my 2015 Macintosh. It crashed the first time I ran the game and never started after that.
If you want to get into modding your options are:
Mod your own console if it’s compatible.
You will have to have a specific model of the 360.
You will need moderate knowledge of soldering and wiring schematics/circuit boards.
There is extensive information about this on Se7ensins.
Purchase a JTAG’ed Xbox 360
There are many people who buy old 360s and JTAG(mod) them as a business.