I have my gaming PC in the next room to our daughter, she's 4 at the end of January & I never used to need to pussyfoot around her & turn it down. She goes to bed at 7 (we don't make her sleep at 7 if she wants to watch something in bed though) and sleeps just fine even if I fire up a noisy game with the sound cranked up.
We can go in her room & put clothes in her wardrobe etc and it only disturbs her if it's morning, some kids are just really heavy sleepers.
She only really wakes up in the night now if she has a bad dream or needs the toilet, with the latter she just sorts herself out.