A little late to help out the poster, but I have made quite a few OEM gaming boxes and HTPCs recently from refurbs (or just discards). They definitely work much better than the OEM systems of yesteryear. The biggest problem with gaming on OEM boxes of generations past was that even budget GPUs required 6 pin PSU connectors, and upgrading the PSU had an added cost and compatibility issues.
If you are sticking to the 75W available on the PCIE bus and no need for the 6 pin connector, yes, OEM systems have work out much better than they used to with something like a 1050ti.
Where you will run into problems is trying to go past the 1050ti into the 1060 range with the additional power (and cooling) requirements, necessitating a new PSU and case.
I built an Optiplex 3010 for my son with an i5-2300, 8GB of ram, and a low-profile 1050ti. Hes not that old and mostly plays lego games/minecraft, but it works very well for that and by the time he outgrows it it will be time to build a new system. It would be plenty capable of playing many other AAA games of 2016-2017 at 1080p as well.
Another system I've built is the retired workstation (Dell T3400, T3500, T5400). You can often get cheap xeon upgrades for them and sometimes the ECC ram can be much cheaper than non-ECC counterparts as they are from retired servers with limited market. The power supplies are often 600-800W and have the 6pin PCIE connector. They are nearing the end of their useful life and you'll find plenty of games to be CPU limited, but they are a very good option if you want a low cost of entry into the game.
Plus the front panel of the dell workstations comes off pretty easily and you can do some interesting custom paint jobs.