Honestly, I'm a huge fan of the original RE series and while I was able to push through and evade Mr. X, I do find his inclusion hugely stressful, and slightly misplaced in a game already dripping with more subtle, moment to moment tension.
Stalker mechanics are very divisive - and these are amped-up in RE2 by adding them to an area already littered with plenty of other lethal enemies. While the classic RE series did have recurrent enemies of a sort, they never had anything like this type of design (whatever the reasons might have been).
Were the game not so polished in other ways, it might well have put me off too - I think it's fair that some people will be put off by this, particularly considering that the closest similarity from earlier REs is that one mine section in REmake with Lisa Trevor, which is on nothing like the same level.
It does make for some great emergent gameplay moments and clearly it was designed to be the way it is, so this isn't a qualitative assessment from on my part, but I honestly think some people being annoyed is understandable.
