If you want to keep costs down no you don't need an i7 for gaming. Most games won't utilize all the cores anyway i5 is fine. 1050 is more than enough to play AAA games maybe not at ultra. But I can play GTA5 on my 14" ultrabook with mx150 graphics and get a pleasant experience.
I'd look at Dell's inspiron gaming series. They have good spec/value and don't look like the typical ROG or MSI gamer style.