Except Crysis 2, which uses the completely different CryEngine, seems the exact same problems.
I have a dual core H3220 for my HTPC while my main PC uses a 4770k. I can confirm that crysis 2 and crysis 3 really need a quad core minimum (logical or physical). However, this is an exception, not the rule. I've played tons of games on my HTPC, and crysis 2/3 are the only ones that cannot play well on dual cores. Literally every other game i've tried has been butter with a dGPU. Now I have seen i3's playing crysis 3 as well and they generally do just fine. Being that the i3 has HT, it will run crysis 3 fine. But crysis 3 at high/ultra settings on a pentium doesn't really cut it, you do have to lower settings. It's a cryengine thing.
Cryengine really needs a quad core feeding it, but having played tons of other modern games on my HTPC they really do all run great with a dGPU. I was just playing Batman: AC on it the other day and my framerates were near 100 most of the time, same for Witcher 2. Witcher 2 is always north of 60 fps with near everything dialed up except uber sampling. Saints Row 3/4, sleeping dogs, and tomb raider all played amazingly well on this HTPC as well, I should add.
So far crysis 3 is the sole exception to the rule that i've found. With a dGPU, the dual core pentiums really are great. Although these days, they're not amazingly cheaper than i3's, but I wanted the g3220 for my HTPC. I got a pretty sick deal on the g3220 with h81 mobo at the time (around 100$) so it was something I couldn't really refuse. It games VERY VERY well with a dGPU.
So what i'm getting at here is characterizing a dual core as unsuitable for gaming, that is not the case at all. Not even close to being the case. Basically, cry engine has to be lowered in settings to work on a dual core without HT. But I haven't found other games that are like that. If there are lemme know and I can probably give them a whirl and check, but so far, I've been more than impressed with the G3220. I threw a 780 in that rig for a day and couldn't believe the framerates that all of the games were getting. Quite impressive to say the least. It doesn't replace my main PC, of course, but the G3220 is pretty amazing nonetheless; i'm very interested in seeing how well the unlocked pentiums overclock. I wouldn't hesitate for a second in buying one as a replacement for a htpc/gaming rig after seeing what the Haswell pentiums can do.