This これが is indeed tricky, and it somehow sounds almost the same as saying こんな状況で to me. This これが is like saying "in a situation like this", "see what's going on", "look", "come on" or something. This usually appears in a rhetorical question pattern, これが + ~て/ないで/ずに + いられるか/いられようか
.
- これが笑わないでいられようか。
How can I not laugh at this (news/situation)?
- これが飲まずにいられるか!
How can I refrain from drinking (alcohol) in a (sad) situation like this?
→ I can't help but drink on a day like this!
- これが落ち着いて(い)られるかよ!
Hey, how can I stay calm now?
- これが喜ばずにいられると思うかい?
In a situation like this, do you think I can keep being not pleased?
→ Come on, how can I be not pleased?
As you can see in the second example, this type of これ is clearly not the subject nor the object of the following verb. But rather than trying to analyze further, I think it's best to memorize this これが is almost like a fixed guiding adverb that indicates いられるか is coming and strengthens the meaning of the rhetorical question.
これを喜ばずにいられると思うかい and これに喜ばずにいられると思うかい are also correct and make sense, but これが sounds more idiomatic and natural to me.
You may know this, but これが and それが also work like a conjunction meaning "however", "actually" or "despite your expectation":