A Mary Sue is a character that, as another poster put it, "A character who is overly perfect and fits into the story in an unrealistic manner". It's hard to claim a game-based character is featured in an unrealistic manner since they often have to be.
This, just about. I disagree on the "overly perfect" requirement, but the "fits into the story in an unrealistic manner" bit is pretty much spot on. Sure, the "God Mode" and "Purity" Sue varieties are almost certainly the most common; I'd argue that, for example, pretty much all of
Pokemon's league-only-type rivals qualify as one or the other, Tobias being most obvious, considering their tendency to exist solely as a means--a "diabolus ex machina," or "devil out of the machine," if you will--to make the appropriate main character lose in their region-ending tournament arc. But whether or not the character exists unrealistically--in particular, whether or not they warp the nature of the world or the characters within the story--is far more important; otherwise, the various Sue varieties that
do have flaws (for instance, the Anti-Sue, a character whose creation process may as well have involved the author perusing a checklist of common Sue qualities and going "Oh, well, I'll just make my character the exact opposite of
all of this!" and yet falls into the
exact same pitfalls as other Sues) probably wouldn't be as well-recognized.
Take, for instance, Dr. Gregory House. Perfect? No; even though he's supposed to be very good at what he does, he doesn't always get the right answer, and when he does, it's after he's spent the other forty-odd minutes of the episode coming up with the wrong one. Attractive? Well, that depends on your opinion of Hugh Laurie with a bum leg and a permanent five o'clock shadow. Nice guy? Quite the opposite; he frequently bullies not only his employees, but also his patients, his boss, his best friend...he's a jerk. A lonely, borderline-crippled, pill-popping jerk. A genuinely flawed character.
But here's the thing: he's still a Sue (Stu for the politically correct)--at least, I believe he is. Why? Because he's a jerk--or rather, because he's a jerk and
gets away with it, even though he really shouldn't. His team of employees respect him. His boss is practically in love with him. His best friend is still his best friend. His patients...well, okay, there's been mention that the hospital only keeps House around because he's "Just That Good" and has part of its budget set aside solely to deal with lawsuits against him, but those are more likely from the genuinely stupid "Johnny Everyman" clinic patients that he regularly insults, as opposed to the patients-of-the-week with actual life-threatening conditions;
they're typically nothing but grateful that he saved their life. But personally, I should think that his skill level
wouldn't take precedent over the fact that he's a drug addict who not only regularly orders/performs risky and unethical if not illegal medical procedures (and bullies his boss into letting him do them), but has done
numerous other things that, in the real world (which is where the show ostensibly takes place), would have not only gotten him fired from the hospital and his license to practice medicine revoked, but landed his sorry tush in prison for any number of years.
Sorry, got a bit ranty there. Point is, a character can still possess genuine flaws and still be a Sue.
Conversely, a character can possess no immediately visible flaws and yet
not be a Sue. Like Cynthia; lacking in flaws, to be sure, but considering her role as one of the most powerful trainers in the franchise (just like all the other Champions), it's honestly very much to be expected.
And--though this may be more of a personal thing--it's also possible to still enjoy a character even if they're almost undeniably a Sue of some sort. Like, I still enjoy (well, enjoy
ed, at least) House's character despite the above criticisms, and the main reason I like Tobias as much as I do is
because he's such a blatant Sue; he just wouldn't have had the same effect if he'd been "just another" league-only rival. And hell, what about Paul? Biggest Jerk Sue-type character in the entire show right there, and just
look at how much love he gets!
'Course, with all that said, yes, you all
do have something of a collective tendency to use "Mary Sue" (and her older, hotter sister, "Deus ex Machina") as shorthand for "I don't like this character or how they did this or that thing or behave in a way I don't like, but because I don't feel like expending five brain cells on attempting to provide a cohesive, logical argument, here's a lame, misused blanket term."
Seriously, stop it.
The Great Butler said:
Evasion, Double Team, Minimize, etc. And that's different than using a move in a completely impossible way, which is closer to Ash's cheating in the second Anabel match by recalling and immediately reusing Corphish, AIM FOR THE HORN, Thunder Armor, or any of the other times an immunity is ignored.
Not to mention that the show's "dodge" mechanic has effectively been worked into the games; when a move misses, the message no longer says "[move] missed!" but rather, "[Pokemon] avoided the attack!", with the implication that you're supposed to imagine them actually dodging the move as opposed to just standing still and trading blows (which the older games apparently had them doing).