There are two sides to this coin
I fought a long war of attrition with our CEO in one of my jobs that I am NOT going to restrict gaming _AFTER_ hours provided that they have done their job by then. Not now, not ever.
Leaving them to play helped me debug quite a few firewall issues, ensure that the network monitoring is up to scratch, QoS and bandwidth slicing and dicing on the firewall works "as advertised" and the whole system functions the way it should be.
We had that recurring conversation every week along the same lines: "Q: When are you going to forbid games on the company network. A: I will not, I have a free test and performance team, you either hire an equivalent and pay for equivalent tools (here is a quote for 20k for you to consider) or let them continue doing their job for free".
That, however, was the development team (not the IT). They also delivered everything they were supposed to deliver by 6 at which point they downed tools and the shootout began.