So as others have said, if all you’re doing is playing games it’s probably mostly fine. It might struggle a bit with some more CPU bound titles, but most modern games aren’t *that* CPU hungry. That said, that’s my recommendation if you’re going for a budget build. If you’re planning to pair that with a 3080 or 6800 I’d call that a bit a silly, if you’re already spending that much on a GPU you might as well get an adequate CPU for it too (though by all means, if you already have the system first check if you’re actually having any problems – first rule of upgrading, don’t upgrade just for the sake of it, upgrade to fix a problem you’re having).
Also just to be clear, modern CPUs are way better than the 2013 models. The question is just if games actually take advantage of that, for which the answer is still mostly "err, not really" especially if you’re playing at higher graphics settings. That’s why it’s not necessarily necessary to upgrade if game performance is all you care about.
Peripheral wise this also limits the kinds of MBs you’re going to get, which’ll limit you in terms of that... but I’m just gonna go on a limp and assume that if you’re being this thrifty with your CPU you don’t feel a strong need e.g. for PCIe 4, more PCIe lanes or USB 3.2 either.