To be fair, I do NOT think the gaming performance of a QUAD CORE LGA775/771 system is terrible. You can play at 4K in games at 30 FPS and get a modern console experience out of your machine. And it still has benefits over console (such as multi-tasking, web browsing, etc.)
However, I cannot recommend anyone buy a system like this, as games like AC Origins and Apex Legends (just to throw a couple out there) will not run. This isn't because the processor isn't powerful enough, but rather it is missing an instruction that is critical to the game.
Now you may argue they should be able to allow some sort of emulation for this for a processor that is missing these instructions, but most people have moved forward from the LGA775/771 systems, and they would be wasting resources on something that is used by a very discrete minority, which is ineffective compared to the other things they can address such as improvements in gameplay, graphics, etc.
I understand it is frustrating to want to play a game and not be able to. My recommendation is to maybe try a cloud service, such as shadow. Shadow is $35 (USD) a month and allows you to play on another computer in the cloud with very minimal latency. Other than this, you could try emulating POPCNT yourself, but this WILL decrease performance.
I have a few LGA775 systems that I tinker with. They aren't that bad. Running games at 30 FPS isn't the end of the world. But I have noticed, even with an Intel Xeon X5470 Overclocked to 3.5 GHz (I have a potato motherboard; 4 Cores) and a AMD Sapphire R9 Fury 4G, it still struggles to get decent framerates, especially in open world games. (GTA V for example runs between 30 FPS and 60 FPS, but usually hangs around 40 FPS).
To be clear: I think it's awesome that computers over a decade old are able to run modern games. It's like a slap to the face for the console users, who are just now getting 4K and have to pay $500 (USD) to get it, where as you can slap a computer like this together for way cheaper and get the same experience. But you can't argue the system is not obsolete. Once you are unable to do a large variety of tasks (without emulation), it should be considered obsolete.
Finally, I would just like to say: I hope someday that CPU instructions are more easily emulated for those non-tech savvy folks out there, but if you can understand this, you may be able to play: https://software.intel.com/en-us/articles/intel-software-development-emulator