Plus, people might consider NOT playing with your phone during dinner a really delightful thing. (My wife would be proud of me mentioning this, not that I tend to be that polite most of the time..)
As for the rest, of course it's rude to be "playing with your phone" during dinner, and while it's sometimes necessary to initiate or answer some communication, to leave the table before doing so is only polite. But rudeness in response to rudeness is rudeness nonetheless, and justified only in the face of extreme provocation; such a minor impoliteness as the one we're discussing is far more pleasantly and effectively dissuaded by a polite response than a rude one -- something which, it seems to me, "I will disallow anyone..." evinces a certain failure to grasp.
If you want to do all that, stay at home alone and do it on your PC. If you want to enjoy a meal in the company of friends, then try to live a bit more in the moment.
Stop projecting your emotional state onto other people.
To me, the biggest difference between childhood and adulthood is that adults have real responsibilities that are more important than silly games.
Do you look at that incoming email that isn't from the on-call address? Do you just check for new messages even when nobody is calling? Do you look at your twitter feed? Facebook? Just a quick check onto a favorite web site? Tap out replies to anything except on-call or your wife?
It could be that you're the exception - maybe you do only respond when you hear the special notification sound for your wife or the on-call originating address. I'm dubious - but that's colored by my own experience. I thought much the same of myself until I actually stopped and paid attention to what I was doing with my phone when around others.
A lot of times though, in a lunch-with-coworkers situation, we just run out of things to talk about and check our phones sometimes and that's okay.