What is its called when you buy a program or game and you can't use it anymore do to the devs shutting down the servers (an online game in my case)

You have suffered a withdrawal of service. Whether this is a breach of contract or not depends on the terms of the contract you agreed to by ticking the I confirm that I have read and agreed to the terms of service box when you bought the game.

I know most of us never read through that boilerplate text and only understand half of it if we do but it still forms the contract.

Whether you can get any redress depends on the terms of the contract (of which, I presume, you do not have a copy); whether you or your legal representative can contact the development company; and, probably most importantly, whether the company is still trading. I suspect that they may have ceased trading, stopped paying the hosting fees and that the hosting company have shut down their service. Best of luck but I don't hold out much hope.

Obsoleted; Unsupported

Because the developers have shut down, it has become "obsolete" or it has been "obsoleted" by the developers.

Because the developers no longer provide service related to the software, it is an "unsupported" product.

I won't talk about the legal side of the issue, but technically it is called
"online service (was) discontinued".