Pretty good list, only missed some more restricting ones, others not so much. In any case, here:
Game: Set in a game or games are what drive the plot. Examples: No Game No Life, Death Parade.
Demons: Pretty self-explanatory, the show involves characters whose origins are related to demons/non-human. Examples: Hataraku Maou-Sama.
Music: Centralizes around characters who have a distinctive trait of singing/playing some type of instrument. Examples: Shigatsu wa Kimi no Uso, Symphogear GX.
Space: Set in the space (note that not all sci-fi anime are necessarily space anime and vice-versa). Examples: Sidonia no Kishi.
Police: Anime in which police organizations take a major role in the story, usually associated with mystery. Examples: Psycho-Pass, Higurashi, Paranoia Agent.
Thriller: Characterized by scenes where you are constantly thinking "what's about to happen". Often associated with dark themes and even horror. Examples: Higurashi, Shinsekai yori, Monster.
Magic: Revolves around the use of magic, i.e. things that would normally be impossible happen. Examples: Madoka Magica, Fate Series.
Parody: Shows that are full of references to others, usually making fun of them and thus being associated with comedy. Examples: Gintama, Binbougami ga!
Kids: Anime with simplistic plots/often cliche characters that are mainly targeted at kids. Examples: Pokemon, Digimon.
Slice of Life: moeshit Anime in which characters are put together in a scenario (often school/or outside of the city) and live their everyday lives. Most of the scenes are funny or just relaxing to watch. Examples: Barakamon, Gakkougurashi!
Super Power: Characters possess powers that humans normally can't acquire by any means, such as becoming invisible or flying. Often associated with action. Examples: Toaru Series, Hunter x Hunter (2011), Charlotte.
Samurai: Involves characters that are samurais. Often associated with historical themes. Examples: Samurai Champloo.
Vampire: Involves characters that are vampires, in some way. Often associated with horror or excessive amounts of gore. Examples: Shiki, Owari no Seraph.
Fantasy: Anime that are set in places that are so out of this world that it almost seems like it's just a dream fabricated by the protagonist. Usually involves themes that are very common in anime, such as cat girls. Examples: No Game No Life.
Military: Series in which you're shown characters living a military life, which is often rough, not so in others. Examples: Grisaia no Meikyuu/Rakuen, Gate, Fullmetal alchemist.
Also, this one isn't normally seen as a genre, mainly due to how little anime have this type of setting, but here:
Prison: Anime in which the characters are somehow locked away from the outside world/other people. Examples: Deadman Wonderland, Prison School, Rainbow: Nisha.
And finally,
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Dementia: Characterized by having mind-twisting plots and overall creepy atmospheres. Examples: Evangelion, Serial Experiments Lain.