Drama/Tragedy
Well, it's a dramatic one-act play, so "drama" is kind of a no brainer, right? However, Fool for Love is definitely also a tragedy—come on, it's using the same playbook as Oedipus Rex, which is one of the biggies, as tragedies go, so that can't be too big of a shock.
With two protagonists who are totally trapped by their forbidden love for each other and their delusional (and imaginary—he's a delusion himself!) old man rocking away in his chair and talking nonsense about being married to Barbara Mandrell, the play presents a pretty sad-sack set of people and circumstances—and at the end of the play, it's clear that May and Eddie have made zero progress, still up to their old tricks and trapped in their same old toxic, codependent cycle.
Definitely tragic. Definitely squirm-worthy.