The 'rules' of an RPG, if we mean 'all the concepts about the game that have a bearing on how the participants understand the game to be played' are so extensive that for no game have they ever been formalized. As a consequence of this, we are all playing a game which has not been standardized in the rules.
In D&D, the DMG stands as an attempt to - within certain limits - standardize play rules that aren't covered by what we would normally call the formal rules of the game. The DMG gives guidelines on how much treasure is normal, how fast characters should advance in ability, how common magic items should be, what sort of challenges the characters should face and so forth. The longer the game goes, the more it seems that the writers of the DMG see the book as having this primary role and the more they seem to think that uniformity of play experience ought to be an overriding goal. That is to say, the later the edition, the more formalized the guidelines in these areas have tended to become. But for the most part, in any edition they remain guidelines over which the DM asserts a massive amount of personal preference.
And that is to say nothing of the fact that the same DM can run two very different games depending on the play style of his players, over which he can assert relatively little control.
To attempt to answer your first question, what other games give such a huge variance in play experience, I would suggest we imagine a situation where games are not standardized by Hoyle or others, and we each learn to play 'Cards' by sitting at tables and having the rules communicated to us through play.
Quite obviously, if we consider 'Cards' to be a game, then the variance in play style is huge. Even if we consider 'Cards' to be more analogous to RPG's in general, the variation in non-standardized versions of games like Hearts, Poker, and Canasta is considerable. In fact, my family plays a version of Canasta which is pretty much unique to my family and is based on certain misreadings/misunderstandings of the standardized rules plus some odd house rules which improved the standard game (in our opinion) and so were left in. (For those that are card buffs, the version of Canasta I was brought up playing is closest to the standard version of the Canasta variation called 'Hand and Foot', although it was independently created and differs in some particulars from that game as well.) Over the years, I've met other canasta players which played variations including one or more of our particular house rules in various combinations, including ones which we invented without a rule book. And considering the number of people who we've taught to play, and the number of people they have taught to play, there is a fairly large number of people who believe that way is 'normal'.
Even monopoly can have wide variation depending on whether you auction properties when the person decides not to buy them, whether you house rule 'free parking', and how cooperatively the players play the game.
So, in practice, I'm not sure that such wide variation in play style is actually unusual. Games tend to be ammendable to house rules. They tend to be learned as much or more by playing or by oral relation from another player rather than by actually reading the rules (and the longer the rules the more this is true). Complex games tend to suffer from multiple misreadings, and these misreadings are likely to persist if the resulting game is non-degenerate. And games which are based on simple generic tools like dice or cards are particularly well-suited to the creation of variants. Since RPG's are basically dice + narration, it's not surprising that the experience of play varies so much.
A drive through order is faster but only correct on a 1-2 on a d6. Going inside is more dangerous and takes longer but you get the order right on a 1-4 on a d6. 
