телезритель (TV), в театре - это тоже зритель
зритель - это общее понятие, не обязательно в кинотеатре

filmgoer/moviegoer - это, якобы, тот, кто ходит в *кинотеатры* и, возможно, *регулярно* - https://en.oxforddictionaries.com/definition/filmgoer

So then what’s wrong with зритель? If you don’t have a specific word for a moviegoer, isn’t someone who goes to the movies regularly a зритель? What else would you suggest?

кинозритель?

"зритель" is a too general term applicable to TV, cinema, concert, show, circus - pretty much to any entertainment. And it doesn't imply any love to movies/cinemas or any regularity. Someone comes to a cinema first time and instantly becomes "зритель"

"кинозритель" - yes, it's "зритель" in a cinema, specific or general, but it doesn't imply regularity either (if it's essential, that I am not sure about).

If regularity is important, I don't know any word in Russian.
There is "кинолюбитель"/"любитель кино" - but this term covers films/movies both/either in cinemas and/or TV.

As a side (irrelevant) note, it's worth saying that "этот фильм понравится кинозрителЮ" means the same as "этот фильм понравится кинозрителЯМ"

The regularity is inconsequential. You mostly hear this expression when they refer to a new movie: “Moviegoers will be treated to the third installment in the Lord of the Rings trilogy this weekend” It just refers to people going to the movies.

Тогда кинозритель.
Если из контекста ясно, что речь идет о кино (как в твоем примере), можно сказать и просто "зритель"

Thank you! Here’s an example, completely disassociated from regular moviegoing: https://www.philstar.com/nation/2018/09/06/1849213/34-moviegoers-arrested-not-standing-sing-lupang-hinirang-inside-cinema