Our eldest was a bit of a fussy eater (like his father was as a child! hasttag Just Saying), wasn't keen on mushy food, strawberry, steamed greens, more a texture thing. So we played the long game, as he was a "eat to live" child we didn't make the dinner table a battle ground. It is also advised, if you can get your child to try things over and over again, so with all this in mind if he ate "one piece of broccoli" or one strawberry, or try a bit of each vegetable, he could go.
It took years. But his relationship with food is ok now, could be better but so much better than we thought was possible (and we still advise and encourage him). Nailing him to a chair, telling him he had to "finish" his plate and he couldn't come back later, was not going to get us anywhere and possibly/likely create a dysfunctional relationship with food. So he could go and come back, he came back to healthy stuff, it wasn't like we gave in and fed him crisps or anything like that.
This was at home.
We explained our technique and reasons when we visited friends and family, and if they had a stay at the table, ours would stay at the table being well behaved but they didn't have to finish their plates, compromise. If needed.
And if we ate out, it was always at a venue that was suitable for their age, time of day, other cliente.
What we did at home had no bearing on anyone else, when our children were young and out they didn't intentionally, and rarely if ever made anyone else's time out miserable. They knew how to behave at pre-school, and school. They are now almost young men and are decent, can take them to any restaurant now to eat, table manners, actually we can take them anywhere and they adapt their behaviour accordingly.
Now when eating with friends they are the ones who now to play a game after dinner and stay at the table being totally entertaining, was this because they came to view the dinner table as a place of fun and relaxation not rules and regulations? They don't have their phones at the table unless we need to QR code an answer in a game or something comes up in conversation that needs a a phone to prove or show it. But they are communal phones.
So what's the problem? What is the actual problem in letting a child leave a dinner table in their own house, because the OP says go and play with their toys which indicates at home.
How a child eats at home and their behaviour around eating in social settings can be, usually are, two completely different issues. And just because you let a child move away from a table doesn't mean they "call the shots".
If you met them OP you would never be able to guess they were "allowed to call the shots" and drift from dinner table when they were young. It's about the end game, turning them into nice adults, how you get there is not a proscribed list of rules that works with every child, every time.