what language technique is this an example of?

Yes, it's a metaphor.

One definition of metaphor: "a figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable.".

A figurative love affair. Not a literal one. So, it fits the definition.

Yes, it's cliché as well, but that does not stop it from being a metaphor.

cliché: "a phrase or opinion that is overused and betrays a lack of original thought.". A metaphor that becomes a cliché is still a metaphor.

Sometimes, the meaning of a phrase changes so much that you cannot guess the meaning of the phrase from the meaning of the component words. That's an idiom (not a cliché).

example of an idiom: I get it (to mean: I understand The meaning of understand is not obvious to a foreigner learning English. That is an English saying).

another one, that's more obvious: Barking up the wrong tree.

"Love affair with theatre" - is not an idiom. It is a figurative (specifically - metaphorical) use. Pretending that "theatre" is human and capable of reciprocal love.

It'd be a metaphor if using "to have a love affair with" in that way weren't already a cliché. Metaphors stop being metaphors when they become so used that they stop evoking the imagery their literal meanings connote and thus become clichés.

It's just words in a row.