Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Rough and A Little Too Ready (To Be Violent/Get Busy with Your Sibling); Sad
It's sad times in this rundown motel room—that's clear from the get-go. As we've already said elsewhere, the play is a tragedy, and our characters are pretty sad individuals. Sure, lots of people aren't able to find the strength to get out of bad relationships, but a bad relationship with someone you found out is your sibling? That's a whole new level of sad, pathetic, and awful.
On top of the depressing subject matter and the sad, weak characters, there's an undercurrent of violence/violent tendencies in the characters that feels like it could burst out at any moment. Take a weird interaction between Eddie and May (and there are so many) early in the play, in which May says she thinks Eddie is going to "erase" her:
MAY: You're gonna' erase me.
EDDIE: What're you talking about?
MAY: You're either gonna' erase me or have me erased.
EDDIE: Why would I want that? Are you kidding?
MAY: Because I'm in the way. (27-31)
That's a pretty bizarre thing to come out with out of the blue, right? Okay, cheating is certainly bad, and sleeping with your sibling is really bad, but to just assume that your lover would be willing to "disappear you" crime lord-style is super unsettling.
Then, of course, there are the various threats that Eddie makes against Martin, and May makes against the Countess—they're both super jealous and tend to burst out with promises of violence against their sibling-lover's lovers.
In short, it's pretty chilling how ready these characters are to threaten violence or believe that they will be the victims of it. So, there's this edge of danger and violence in the tone that, combined with the tragic stuff, makes the play a pretty squirm-worthy read.