Okama Hand Gesture (Back of Hand Against Opposite Cheek)

In Japanese, placing the back of your hand against your opposing check is a gesture used to say (or ask if) someone is an okama オカマ, which is a term for effeminate and gay men, and trans women, sometimes considered pejorative.

Gesturer: Otonashi Yuzuru 音無結弦
Retorter: Hinata Hideki 日向秀樹
Anime: Angel Beats! (Episode 4)

Disambiguation

Although this gesture is used to say a guy is interested in guys, i.e. that he's gay, it means specifically okama, and there's a different gesture that means homosexual done by making two finger guns and placing one index finger on the other hand's palm.^{(life.letibee.com)}

As for why it means okama, it's probably because of expressions like "he plays for the other team" being euphemisms for liking men like women do, which in Japanese translate to saying some is of "this side," "that side," kocchi, acchi こっち, あっち.

kocchi-kei
こっち系
This-side type. (literally.)
Someone who is gay, or someone who is a part of the yakuza, i.e. a criminal.^{(detail.chiebukuro.yahoo.co.jp)}
- i.e. someone on the side of women, or on the dark side.

Examples

For reference, some examples of the gesture being used in anime:

Gesturer: Isshiki Makoto 一色誠
Retorter: Togashi Yuuta 富樫勇太
Anime: Chuunibyou demo Koi ga Shitai! 中二病でも恋がしたい！ (Episode 1)

Context: Isshiki Makoto 一色誠 asks Togashi Yuuta 富樫勇太 about his relationship with a (troublesome) girl. Yuuta firmly denies having any relationship with her at all, prompting Makoto to question his sexuality.
nanda, omae moshikashite...
なんだ、お前もしかして･･･
What is [it], could it be that you [are]...
*gestures*
...kore ka?
･･･これか？
...this?
- i.e. "are you actually into dudes, no judgement." (translation used in the English dub.)
chigau!
違う！
[No]!

Gesturer: Otonashi Yuzuru 音無結弦
Retorter: Hinata Hideki 日向秀樹
Anime: Angel Beats! (Episode 4)

Context: Hinata Hideki 日向秀樹 asks Otonashi Yuzuru 音無結弦 to play baseball, with a very specific phrase.
ore niwa omae ga hitsuyou da
俺にはお前が必要だ
To me, you are necessary. (literally.)
I need you.
(double subject construction with dative large subject.)
*gestures*
kore na no ka?
これなのか？
Is [it] this? (literally.)
- i.e. is this a confession of love?
chigee yo, chiimu no koto da yo
ちげーよ、チームのことだよ
[No]!, [I'm] talking about the team!
- You're necessary in the baseball team.
- chigee - relaxed pronunciation of chigau.