There's plenty of games to fill that criteria.
Practically all racing, fighting and puzzle games ever made barely have dialogue or are limited to simplistic descriptions of characters, items and gear and so on (and if there's a 'campaign' mode, just ignore it). There's also good ol' Beat 'em Ups, Shooters, and other arcade-style, usually fast-paced or simple / straightforward games that barely ask anything else from your brain other than to just look at the screen and press buttons on your controller. There's literally thousands of games like that out there. Heck, in recent years we've even got some games that are primarily single-player with a long campaign also have a multiplayer mode where you can just kill stuff that moves that isn't you or your teammate when there's one, such as Mass Effect 3's MP mode, or Dragon Age Inquisition's, to just name those two (or Uncharted 4, etc).
But to answer your question: mostly no. I'm not bothered by games with a lot of dialogue if it's good (well-written, directed, etc).
I do, however, sometimes get bored of too much text-based stuff to read especially when there's absolute zero voice to accompany said text. For example, those bazillion books we can read in the Elder Scrolls series, I'll never read all of them nor do I care to. I did read a couple of them even if most of them are "just" a couple of pages-long; I just can't care enough to literally read all of them or have the actual interest in doing it (but all the honest props go to whomever took the time to actually write that stuff during development). When it comes to text-based adventure / action adventure / American, European or Japanese RPG games I've given enough to the cause during the early-to-mid 1990s when I was into that stuff and had enough attention span to care about each one of those games.
Nowadays I can only care enough to read a few paragraphs at most, otherwise I start to nod off as my brain demands way more stimuli to even function. I need on-screen motion and voice for story-telling or I'm practically out of it, unless the context for reading long texts fits with the situation very well.Games like Witcher 3 or the Mass Effect series, for example, those I'm fine with (or Elder Scrolls, Fallout 3 and 4, etc), only because the dialogue (voiced, or text-based) is usually short-term. I don't mind and do enjoy hearing or reading for an NPCs story or quest-giving dialogue, maybe reply to him/her with my character and just move on to the "action", that's fine. I'm only referring to games where dialogue is predominantly featured and walls of text or even very long-lasting conversations drag on for a century. Now, those games... nah, usually not my stuff at this point.
So yeah and no kind of (voice acting dialogue, sure thing; long-lasting text-based stuff, ain't got the time or the patience for that anymore).