I started with an i3 alpha and put in an i5-4590T. It runs great, but I really cant say if games will run better. I got a base model Alpha for pretty cheap and installed 16gig ram, SSD, and new processor the day I got it. I use my Alpha mostly for work and don't really game on it that much. I just really like the small form factor.

Here is the processor used on eBay. I bought it used also. I don't think you can find this one new. http://www.ebay.com/itm/Intel-SR1S6-Core-i5-4590T-2-0GHz-6M-L3-Cache-LGA1150-Haswell-GT2-CPU-/191903617137?hash=item2cae58d071:g:EikAAOSwc1FXawq7

This i5-4590s should perform about the same in the Alpha and is new on Amazon. I believe it actually gets downclocked in the Alpha to perform about the same as the t version. https://www.amazon.com/Intel-i5-4590S-BX80646I54590S-Processor-Cache/dp/B00J6F5LHM/ref=sr_1_2?ie=UTF8&qid=1467149364&sr=8-2&keywords=i5+4590t