Not workplace appropriate
As someone who has worked in IT for 18+ years, I can say that businesses do not like games on their computers. And for good reason. The business owns the PC and is responsible for it. And for the network that game communicates over.
Therefore, IT divisions are, as a rule, fairly paranoid about these things. Most large companies will have very strict policies and procedures to get software approved through. IT must review the software, determine any risk it presents to the business (both from an IT security risk and a legal risk), and then determine how to license it for those PCs.
Some small companies don't seem to mind. But larger companies will consider this grounds to shut down your network access and can possibly even result in you being fired.
Some businesses might let you use their facility / internet service if the game is on your device (console or your home PC) but again, most won't like that either. Especially the home PC, since, again, the IT department cannot be sure your PC meets their rules for IT security. Bringing in a home PC elevates the risk to them, since it could bring a virus into their network.
If the game's rating is anything worse than T (Teen), then it could also involve someone filing a complaint with HR. Then again, if you get exciting while playing computer games (because gamers sometimes like to yell or cuss while gaming), this too could lead to complaints.
Check to see if your company has an acceptable use policy for IT equipment. Most larger businesses do. That will tell you how they view such things.
If there is no such policy, ask IT. But do so casually, in an non-official manner. "Hey, what's our rule on installing games on our PCs and playing them after hours?" If they don't say no, then you can make an official request.
But most businesses do not approve of such things.