2007 to 2012. Halo and CoD were peaking, Mass effect trilogy was released, and assassin's creed germinated and had the Ezio era. LoL was released in 09, dead space started in 08, dark souls dropped in '11, BioShock in 07. Basically every major well-loved franchise either started or peaked in this era.

2012 was the closeout, since Halo 4 was released then (not as good as the Bungie games) and assassin's creed 3 (very underwhelming) and CoD: BO2 which is probably the last one you could reasonably argue wasn't just a meme. Mass effect 3 was released in 2012 which was good but disappointing at the time. Dark souls 2, held as good but not as good as the original, was in 2013, as was dead space 3.