Will this Macbook pro be able to play Minecraft, League of Legends, and World of Warcraft?

I want to get the non retina display model that came out in 2012.

2.5GHz Dual-core Intel Core i5, Turbo Boost up to 3.1GHz
4GB 1600MHz DDR3 SDRAM - 2x2GB
500GB Serial ATA Drive @ 5400 rpm

Those are the specs but I will be changing it to 8 GB RAM, which is my main reason of keeping it the non-retina edition. I don't mind toning down the settings abit.

Probably not very well at all. You're buying something without dedicated graphics, and Intel HD graphics at that.

On my old HP laptop before I got into building computers, I could still play Minecraft, and WoW (tried LoL once and it was having trouble). But I'd experience lag spikes somewhat often and had to run on low resolution (1280x720 or lower) with lowest possible settings. Though, the laptop had an APU inside of it which is more powerful than Intel graphics. So it will run worst than what I experienced.

Don't expect to do much.