Before you compare and set an expectation, do you have info on the other systems that claimed to have 120fps?
You also mentioned other games run seamlessly, what games are those?
Have you bench tested your system?
With the info you given, I'd say start with resetting cs settings and clear launch.
If no go, double check nvidia global settings and cs:go settings,drivers.
Install fresh csgo.
Playing in Fullscreen could give more fps but most likely not the solution. I assume you have changed 'fps_max x'
Ultimately i think you should overclock the cpu just a bit if you have hardware to support. its free performance unused. That being said, its an old cpu about a decade old so if its an option maybe consider getting a new computer that can...