Oh this is us too! Moo is not even 10 months and he'll go crawling off into the other room all the time. Mostly not too far, but if he gets too quiet I peek in on him.
As an aside... the other day he figured out how to get into the bathroom cabinet where I keep my hair stuff (headbands and hairbrushes mostly), and went to work teasing out a few of my purple clip-in hair extensions, strand by strand. Things got too quiet and when I went around the corner to check on him, I was nearly on top of him before he noticed I was there, and he jumped out of his skin when I quietly asked what he was doing!! ROTFL Needless to say I have re-baby-proofed everything again and changed up the cabinet locks for stronger models.
That said, OP, I really think you should trust your instincts. Every single kiddo is different and a mama's own worst enemy is second-guessing her own mama-gut. Stairs would freak me out, depending on how stable and sturdy he is. Keeping a close eye on your LO can never be a bad thing... unless of course he's like... 20? LOL
My issue isn't so much with him going to another room to play; he has done that on occasion from a pretty young age too. I am just used to one floor living, so he was always close by. In this situation, he is way further away than I am used to...Now that the novelty has worn off, more often than not he wants me to go with him, but there was a solid few days that he would just take off down stairs without so much as a hint that he was thinking of it. (He is very sturdy on stairs). He would stay down there for much longer than he was willing to play in his room alone, so I was just curious how far away and for how long most other kids played....