Are there some plays that are only meant to be read (not for the theatre)

[WaterBird]

I enjoy writing fiction in my spare time, which is more of a narrative style.
Recently, I've started taking a course where we will write plays. So far, we have just done some very small dialogues between characters to practice the writing style. I guess I just feel a bit odd about the fact that my character interactions (which can sometimes be private/personal conversations between them), are supposed to be performed for an audience.
Can a book be written in play format without the intention that it will be performed/acted?

Yes - plays written to be read not performed have their own genre: 'closet drama'.

They are typically long poems written in the form of plays - things like Samson Agonistes by Milton or Manfred by Lord Byron.

Thanks.
Do people still write closet dramas these days?

Not that I'm aware of - they were fashionable in the C19th, but have fallen out of favour since then.

Thanks, that's really interesting that they just fell out of fashion.

Would a play for radio come under this too?

Wasn't there a bit in Educating Rita about 'how would you overcome the staging difficulties of ?' and Rita's original answer was 'Do it on the Radio' or something?