Depends on what you’re replacing. Running & jumping in place on a trampoline won’t match up to actually running (whether on a treadmill or outside). You should try running outside, just be aware that if you’re used to a treadmill doing your pacing for you, running outside will feel difficult because you have to pace yourself. But if you do, say, HIIT exercises, there’s no reason why it can’t be just as effective at home. The difference may be that without a gym instructor keeping you accountable, you might be inclined to half-arse things, or give up a bit earlier than you would otherwise, that sort of thing, but that’s just a individual thing
Whereas for me, I’m a powerlifter. I can’t recreate deadlifts and heavy back squats at home. Holding an 11kg bag of rice and squatting is alright, but it’s obviously not the same as a 20kg bar loaded up with another 30kg+ of plates.