Is there a difference in nuance if I say "sit on my chair" instead of "sit in my chair"?
Yes, there is a difference in nuance if you say "sit on my chair" instead of "sit in my chair". To "sit in" a chair usually implies that the chair is a larger, more comfortable chair with armrests that you sit down further in. If the chair has a harder surface and no armrests, it is more common to say "sit on", since you are sitting on the surface of the chair and you do not sink very far down into it. In the case of the video here, Joey says "sit in my chair", which implies that his chair is a comfortable chair with cushions and armrests.