Here being a プロゲーマー (pro gamer) is a very popular thing among younger people.
The other one (programmer) is written as プログラッマー.
In Japanese both are easily distinguishable, but in English writing "progamer" without a space also made me think it's a typo on "programmer".
The thing is, the Japanese language uses no spaces between words at all, which leads to confusion when learning English, which is a language that heavily depends on spaces.
As I said above, the intention of the student was "pro gamer", but didn't include a space because in Japanese spaces are not used, and resulted them into thinking it's written "progamer".
The teacher (can't confirm, but it's commonly the case) is most likely coming from an English speaking country, and therefore might be unaware of such mistakes to happen, and therefore thought the intention was "programmer".
