Is it worth building new CPU with this specification?

For a gaming machine, little emphasis is put onto the cpu load, with the gpu/ graphics card being the workhorse.
You could easily run a top end i3 and get a beast of a graphics card, but the dual core i3 might not be as good as the quad core in a handful of games. The i5 is the solid choice as it offers quad core, which come in handy for a few games that actually run off more than one core, usually two. Most games out today don't even utilize four cores yet. While some might, it will years from now hopefully be mainly quad core support for games. The i7 is great, but its a quad core with hyper threading. 'Almost' like an 8 core, but since only a few games even use more than 2 cores, none that I know that use more than 4 cores, getting the i7 isn't really worth it for gaming. Applications in which the i7 are used fully would be like video rendering, cad usage, and other high cpu demanding applications. But gaming is more gpu demanding than cpu. i5 offers great strong quad core chip at about $100 less than the i7, so gaming wise, i5 is overkill but will hopefully be fully utilized in a few years. Spend that extra $100 on the gpu, which will be used 100% now, during gaming.

*Edit*
I use a fx 8350, 8 core at 5ghz overclocked. Now my cores aren't as strong as the i5 cores, but that's not what im trying to push here. With my chip when I play games such as bf4 and cod, games normally run 2 cores, and less than 50%. My gpu is a gtx 770 and that runs at 100%, my old 7870 also ran 100% but lower fps, my other machine i7 4770k and gtx 780 i7 runs 2 cores around 40% and gpu 100%. So just showing you that either chip runs at about 1/4 its potential on todays most played games, yet any gpu you get will run at 100%, but the better gpu you get that 100% will result in higher fps. I'd recommend at least playing at 60 fps, as that's the refresh rate of most monitors. Sometimes that means lowering graphics settings from ultra to high, or high to medium in order to play at those 60 fps range. So the better the gpu, the better the playing resolution will be.

For instance, 7870 is $200, and net me lets say high graphics at 60fps, now 770 is $300 but nets me ultra graphics at 60 fps or high at 90 fps. See what that $100 offers, same frames at higher settings, or same setting at higher frames.

Now i5 vs i7, theoretical here. But i5 and 770 may get high 90 ultra 60, i7 and 770 may get high 95 or ultra 65. So $100 more on that processor nets you like 5 fps more.

Now staying at price, i5 and 770 gets you high at 90fps or ultra at 60fps. i7 and 7870 gets you high at 65fps or ultra at 35fps.
*this is why for gaming, i5 and the next step up graphics card is preferred over i7 and a lower gpu