I think you should raise your child how you want. Just tell your Mom "If I mess him up, I'll have to deal with the consequences, not you." I know you're not going to mess him up, but I think that might make her ease up. As long as you aren't one of those parents who ignores their kid when they're screaming in a place like a restaurant or bookstore, you're doing a good job
And Vegreenmom made a good point. According to studies (came from my Psychology textbook), people feel less satified with their meals when they eat while doing something else. Honestly, some of the only memories I have of my family when I was younger was sitting down for dinner. Once that stopped, my family wasn't as close anymore. Of course, everyone has their own preferences though and I don't want you to feel like I'm forcing this on you. Just an idea
Choking would be my only concern for letting a chld roam while eating, but I think most people have common sense not to feed a child something like hot dog pieces while letting them run free. While it's not a guaranteed choking, sitting while eating them is a choking hazard. Most foods are safe to walk around and eat though.
I don't have children myself, but have 6 nieces and nephews. I was at my sisters house yesterday and she has an (almost) 2 year old daughter, Nadia. She let her sit at her Dora table to eat and she wouldn't sit long enough to take a bite. If your child does eat while wandering, than it's perfectly okay. If he starts to chose playtime over eat-time, then you'll have a problem... which you probably don't need to be told. Your child gets fed = your technique is fine.