There's no quote that can define me as a gamer... To be honest, I don't think there's anything specific that can really define me as a gamer (To most people, I'm defined as a metalhead foremost an alcoholic secondly and rarely will people actually start considering me a gamer... Mostly because outside of other gamers there's not a lot to talk about to actually show any gamer in me outside of walking past a game shop and giving my opinions on games)
I play games for enjoyment.
Whatever form that will take... Be it a good story in an RPG, some good mechanics in an adventure game, smooth controls in a platformer, praying to RNG gods in roguelikes, weighty weaponry in an FPS, the eternal grind in a JRPG, the sense of community in an MMO, the strategic battle in an RTS or the combination of teamwork and decision making in a MOBA.
I will play a wide variety of games, focusing on different aspects to suit whatever mood I'm in.
I typically play on normal/hard difficulties, due to how easy games are these days (Be it simplifying to appeal to a wider audience or just years of skill built up applicable to most games I play) - Heck, I even found Demon's Souls and Dark Souls pretty easy, with just a few annoying to deal with areas/enemies. Though I will on occasion set the difficulty down to easy purely to reduce time spent pointlessly (For example, playing Skyrim on the hardest difficulty is pretty fun until about level 30ish when you become unkillable and the difficulty just gives enemies a billion health so they take forever to kill, even with the strongest weapons possible (Using the best skill potions to make the best skill enchants to do the best upgrades)
I don't play games due to their difficulty (Though Demon's/Dark Souls notorious difficulty did intrigue me), but the challenge can turn a mediocre/repetitive/dull affair into something more fun and thus give more entertainment.
I also don't play for competition too much (I used to play TF2 a LOT, but stopped because of being banned from servers for "Hacking" when I beat people fairly using skill) with Dota being the only competitive game I play currently (While I do also play WoW, I don't PvP in it... Though that's mostly because it's PvP is just so bad and I really hate certain aspects of it)