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1.
A core gamer is someone who plays a larger variety of games than a casual gamer but doesn't play video games with the intensity and dedication of a hardcore gamer.

Using an MMORPG as an example, a core gamer would normally progress through their levels at a steady rate and might join a guild but never divulge too seriously into it or use their guild on occasion, a hardcore gamer would want their guild to be the best and constantly do raids and work out techniques.
Hardcore gamer: "My guild is ranked 400 on the leaderboards, tomorrow we are going to get a new recruit end-game items."

Core gamer: "I play alone/with friends and use my guild for help when I need it, or offer help when others need it but I'm not too concerned with ours being the best."
by Origibro August 05, 2014
 
2.
The bastard middle child of a casual and hardcore gamer. He invests in the formers effort and cries when he dosent get the latter result
core gamer is half the wii audience

the {noob} camper in CoD
by Fourm June 12, 2010