I am a goal-oriented gamer, and I get much the same way. Mindless exploration drives me insane - WHERE am I going? I hate 'meandering' in real life, too. I don't mind if I set out with a clear goal in mind, and end up accumulating many more and taking a few wrong routes and learning new things - but aimlessness drives me crazy. I find it difficult to watch people play a game "wrong". I recently had to sit through my housemate's approach to playing GTA4 - hailing a cab whenever it wasn't a chase mission.
Now, in a social setting, when I'm playing a game like that, sure, I'll play without looking at my cards - I'll play by whatever rules are laid down in front of me - but when something in the game is outright ignored (like the missions in Endless Ocean), it frustrates me. I suppose I *am* Psycho Poker ***** - I have no problem with the players who simply miss hidden content, or skim over the cutscenes, but those who wilfully ignore a distinct piece of the game, and not just for 'a single hand', seem foolish to me.
However... that's just in my own, goal-driven mindset. I know these people aren't fools. If they're having fun, all the more power to them. The majority of casual and non-core gamers (core here referring to the typical audience of the gaming enthusiast press) are "Wanderers" or "Participants" in gaming, whereas most core gamers seem to be "Conquerors" and "Managers". I myself fall under both of these latter terms - and while I wouldn't neglect either of the former, that's only another sign of my completist mindset. What gaming needs is more games that cater to wanderer and participant mindsets - why do you think there are so many gamers who only play World of Warcraft, in which the things you end up doing most are ambling from place to place and chatting to your friends? Conquerors love legendary items and beating raid instances, and managers guide their guilds to success. A game that appeals to all types of gamer, as opposed to the classic "hardcore" and "casual" dichotomy, might just be the way forward...
and as for myself, I have increased awareness of my propensity to be the Psycho Poker *****, and will cease watching my housemate and his cab-hailing ways, lest I wrench the pad from him. XD