1. Guess being arrogant doesn't count, huh?
2. By that definition, Yukari can also be called a Mary Sue. People often portray her as the Touhou version of Kira. "Just as planned" and all that. Even when she loses, it's all according to her plan.
1. Nope, it doesn't, because they're portrayed as being justified in that arrogance.
2. Not really. She didn't want the shrine to get destroyed, yet it did. She's had to run damage control on multiple occasions. She's also portrayed as having several flaws, and is actually disliked by the majority of the cast. There is a difference between fans portraying a character as flawless (in which case they may well qualify as a mary sue... in that particular fan work) and a canonical portayal as such.
1. And why is that any worse than, let's say, Rumia's "dumb man-eater" angle for example?
2. And they did, by getting their sake stolen. Or are you still not satisfied by that?
1. What RRR said, plus the fact that "dumb man-eater" doesn't make a character come off as badass, perfect, superior or what have you.
2. You get, what, one panel of the duo looking constipated as the big payoff for having to deal with lectures on how lunarians are da bomb and the earth is a cess pool, a physical demonstration on how one of them can beat up experienced professionals in an activity they've never tried before without difficulty (and one after the other, no less), and how the other can apparently destroy gensokyo with a wave of a fan. I gotta say, it's not a particularly satisfying ending to the manga.
The written version on the other hand is very satisfying, but then that's more against Eirin.
The whole "most of the people who call them mary sue's are probably ReMariSakuYukaRei fanboys" point is interesting. I don't dispute that there's probably many cases where it's accurate.
On the flipside, most of the time I see people defending the two, I get the distinct feeling they're doing so because they dislike the rocket crew or Yukari, probably because they feel said characters get too much attention that would be better given to their favoured indie characters.
I admit, I like Yukari, and Remilia, and Reimu, Sakuya and Marisa. But my favourite games they appear in are the fighting games, where each one regularly gets trounced, and this doesn't make it any less enjoyable.
Much of the time, the winner even acts a bit smug, but its fine, because they get their own turn to taste dirt. The Watatsuki's just dial that superiority complex up to eleven, without any return except one of their (presumably many) valuable possessions getting stolen, and even that is barely shown. The cast doesn't even react much to this, like it's entierly natural, and it comes off as if the author is going "hey look even dese guys reckon the Watatsuki's are the best, mebbe you should too!".
The whole manga just came off as if it were a bad fanfiction with the Watatsuki's being OCs.
I personally just can't stand when characters act smug or superior and never get pulled down a peg, or when they do, it's brushed aside or done offscreen. If Reimu canonically solved every incident first try through curbstomping all opposition, I'd place her on the same low tier as the Watatsuki. Eirin, due to the fact she essentially wins in IN even when you beat her (IIRC), and thus seems justified in her smugness (further exacerbated by how even the good route only ruins her plans due to Reisen, not any flaw of her own), was one of the very few characters I disliked rather than simply felt indifferent to, but the short description where she tries the moon booze was enough to elevate her to a likable character again. Show me a sequel where the lunarians lose confidence in the two due to letting their booze get stolen and them dealing with the fallout (neatly providing an opportunity to flesh out their characters, hurrah) and I'll stop treating them as mary sues.
Also, more CoLA style stories would be awesome, if they're done to the same standard as the original.