Right now I'm managing to run LoL with a 2005 Acer laptop - albeit at lowest settings and prone to fps drop.
In comparison the machine above would run circles around my "ancient" device.
Pricing wise you're not in a bad spot - In the 90s I invested over 3k in a pentium 2 400 with bells and whistles galore (for the time).
I think it's a bit overkill personally - Newegg has been great to me in the past, but ibuypower doesn't particularly inspire confidence.
If you're planning to build a "series" computer, you're investing a bit much into that one, as that one should be solid unless you want to start getting into overclocking and running dual video cards and all that mess.
If anything my biggest concern whenever building a pc from scratch are the potential compatibility issues - but the keyword is potential. Since you're planning to buy a fully built system that should eliminate most of that worry and as far as LoL goes its plenty powerful.