Will the 2013 macbook air run older games fine?

I built my own desktop with a gtx780. I use it for gaming, but i'm almost never home, and i don't like having a fixed position. I'm getting a 2013 13 inch macbook air, and i was wondering if it would run games like league of legends, starcaft 2, garrys mod, and minecraft. Also, i don't need or want a retina display. So would that macbook with intel i5 and 4 gigs of ram run games decently?

All of the games you listed support Mac OS X. You might want to check the system requirements for each game though

StarCraft 2 https://us.battle.net/support/en/article/starcraft-ii-system-requirements

LoL https://support.leagueoflegends.com/entries/23260481-League-of-Legends-Mac-Client-Minimum-System-Requirements

Garry's Mod http://store.steampowered.com/.../app/4000/

Minecraft https://help.mojang.com/...quirements

Some games might require flash or java. Also try not to run other programs while playing these games due to your low ram size.

Yes it should be.