The entire handwritten list can be found before page 1 in the black sketchbook.
In order to come up with a game type, I researched into and created a list of current ones, along with some examples. Some are obviously more archaic or historic than others. However, some may be considered more as game sub-genres. They are not in alphabetical or particular order:
Platformers
Shooters
Fighting
Roleplaying (RPG) (MMORPG)
Text-based adventure
Turn-based
Shoot 'em up
Beat 'em up
Stealth (Metal Gear Solid) (Assassin's Creed)
Survival
Bullet hell (Cuphead) (Final boss fight in Skylanders: Spyro's Adventure with no jump mechanic)
Rhythm (Guitar Hero) (PaRappa the Rapper) (Dance Dance Revolution)
Visual novel
Dating simulation
Point-and-click adventure (The Walking Dead) (Secret of Monkey Island)
Sandbox
Board/card games
Trivia
Puzzle
Logic
Wargames
Practical (golf, football, rugby, snooker, other sports)
Edu-tainment (Putt-Putt) (Oregon Trail)
Electronic sports
Run 'n gun
Choice
Fantasy
(Feature only) Toys-to-life (Skylanders series) (Disney Infinity)
Action
Racing (Forza) (Need for Speed)
Live-action laserdisc (Mad Dog McCree)