None of that has much to do with performance in gaming titles. If it has integrated graphics, then the model of the i5 has some bearing on it because the CPU model determines WHICH integrated graphics it has and the thread capabilities come into play somewhat on threaded titles, which are less common than single threaded games but still relevant.
The fact is that nearly ALL integrated graphics solutions are WEAK and not capable of playing any REAL games, aside from very low end online games like the facebook and pogo stuff. Any true installed title of any quality at all is going to want to see some minimal form of dedicated graphics card or at the very, very least, one of the extremely few integrated graphics solutions like the HD 4600 and HD 6000 or on the AMD side of things the R5, R6, R7 and R9 Radeon integrated graphics with the R5 being VERY borderline even for low settings on most games.
If you buy a unit with no discreet graphics card, and only integrated CPU onboard graphics, that is not HD 4600, HD 6000, R5, R6 or R7, minimum, you will almost certainly not be satisfied with the way things will go in the majority of game titles, even if you're a somewhat casual gamer.