When you are reading, texting, playing video games on your handheld device, stacking dice, doodling, or doing anything else other than paying attention to the game, does that mean you are bored? Or are you just fidgeting and still paying attention?
I can fiddle with dice, or doodle, and still be paying full attention to the game - rather like I can pay attention to driving and an audiobook at the same time. Different sections of the brain, or something. My wife often has handwork - crochet, most commonly - for much the same reason. Keeping the hands busy can actually increase attention span for some folks.
As a player, I prefer a physical character sheet. As a result, I don't really need (and thus don't have) a laptop, tablet, or other computing device at the table. I only open rulebooks when I'm looking up something relevant for the game.
When hosting the game, I will occasionally step into the adjacent kitchen when it seems play isn't really centered on my character - but that's because I'm playing host, and I feel it is my responsibility to keep the water pitcher filled, hot tea available, or last bits of game-dinner prepped, etc.
How often is that true with you and your DM? If you are not doing it out of boredom, would you be upset if the DM asked you to stop? Not so much the fidgeting stuff (stacking dice, doodling), but would you be upset if the DM asked you to stop texting or reading a book?
I joined a group recently where my wife and I are the only ones who don't have a device at the table. The GM, I'll grant, has use for it.
But one of the others regularly drifts off into dealing with e-mails for other online games, or chat rooms, and loses track of the game events. This player has some other behaviors that just don't go well with my playstyle, though, so I can't tell if my annoyance is really just about the chat.
But, given my annoyance, if I did drift into a behavior that others found annoying, by the gods, yes, I'd want my GM to tell me! I would want to correct my behavior ASAP.
A question for DMs; do you feel it is rude if a player is doing these things? Would you ask him/her to stop?
See above. I find players who drift too far off from the game at hand to be pretty rude. So, if your distraction means the others have to say your name several times to get your attention, or you frequently need recaps of the action, there's a problem. If one of my players was doing so, I'd want to find out why, and discuss the matter.
Some folks are just addicted to connection - those folks just need to put the device away. But, if the problem is that the game is not really floating your boat, then we need to talk so we can see if we can make the game more to your liking, so you don't need extra entertainment at the table.