It has nothing to do with the GOG version. Walking can only be achieved via analogue controls so it is unavailable when playing with keyboard + mouse. The 360 controller is useless for many older games (which use DirectInput, not Xinput). The circular input area of the sticks does not allow for proper diagonal movement in those games plus both triggers are treated as an axis which won't work with games that only support buttons - plus pressing both riggers at once will result in no input from either one. And yeah, using Xpadder is a crappy solution since you won't get to bind analogue controls to the Xbox 360 controller. Bottom line: if you want to play a game like BloodRayne with a controller you will just have to grab another controller which supports DirectInput (there's controllers that support both, though). AFAIK it's triggered at random. Yeah, the combat system in BloodRayne 1 is pretty fucked up. In a German-speaking "bloodpatch community" there was a few files for the game including a patch that restores the swastikas of the console version (and a few nude patches but screw those <.<). Sadly the community doesn't exist anymore and I don't know where you'd find the files now.

Are you sure the shift key (left shift only, perhaps) doesn't toggle between run & walk? I thought it did, but would have to reinstall to check for you.

It's not really random -- it's when, in the rare circumstance you are able to, you go up close to an enemy without them noticing you/going hostile that you can trigger the 1-hit kill attack. It's basically a sort of sneak attack.
Of course, getting it to work is so fidgety and situational that your point about the combat being fucked up still stands :\

Aaaah, THAT attack. I thought he meant one of the stronger "combo" attacks which are triggered in regular combat (and which IIRC are completely random in BR 1). Yeah, true, that one's supposed to be some sort of stealth attack, although occasionally it will be triggered even when frontally attacking an enemy (I presume that the engine sometimes screws up some positional check).