Yeah, making it a requirement to get up from the safety of the table would make it a hard no for me. Since the O/P explicitly asked for games to be played around a table, maybe stick to those that can be played at a table as written?
RPG for 6 players and 1 GM/Facilitator?
Austen: The PromenadingThis is an unplaytested choice but I voted on this game for best 1 day 24-hour rpg on rpggeek.com last year. A large part of it could be played at a hypothetical or even real meal. It’s built as either a larp or epistolary sort of game. It seems like it would work best with even number players.
I will recommend World Wide Wrestling, even for those not into that particular sports-entertainment. Fun, fast and clicks along with a full table of six.
Can confirm: I hadn’t any interest in wrestling since I was like ten but played this a few times a couple years ago with like 8 people and it was an absolute blast! It is perfect for open table play.
Probably too late to help @Eike but recently I ran a one-shot of Knave for a large (>= 6) group of folks new to RPGs and it went really well. I pointed them at a character generator I whipped together and we were off to the races.
I credit the simplicity of the system (rules can be summarized on a couple pages) as well as the fact that random character generation meant we could jump right into the action. I also went around the table doing an exercise to create “bonds” between characters to help figure out who were friends/enemies/etc. which helped gel the scenario fairly quickly.
Noir World would work well with 6. It’s GMless, and people quickly pick up how to do it once the first scene is off.