I think many of you are placing an inordinate amount of emphasis on the CPU. That's only a limitation when detail settings are low, a situation few people play at when they have an i7. Set the resolution to 1080 and detail levels to medium and the bottleneck shifts over to the GPU, just like it's been for years.
http://www.techspot.com/review/921-dragon-age-inquisition-benchmarks/page6.html
http://www.techspot.com/review/1006-the-witcher-3-benchmarks/page5.html
http://www.techspot.com/review/991-gta-5-pc-benchmarks/page6.html
http://www.techspot.com/review/979-battlefield-hardline-benchmarks/page5.html
Nehalem may not be as efficient as Haswell, but IPC can't be much worse than the FX-8350 ( if it's even behind that ), and that chip keeps pace with a 4790K pretty well.
Also, the question was about modern games, which are increasingly going to multi-thread.
Brian, your i7 is fine. The bigger factor is your GPU, especially if you're still using one from the same time you bought the Nehalem. If you've got a current GPU and old-ish i7, you can play just fine. You might give up a little performance, but you asked if it's playable, not if you can max out detail settings.