Collision detection wasn't added to the engine because the developers never saw any need on account of it being a point & click adventure game engine. Collision detection isn't something that really comes up all that often.
The only method I know how is (again) done through scripting. It involves checking if a specified radius value from each characters position comes into contact with another characters radius value. Basically it checks if any of the same co-ordinates inside of each radius is overlapping (the same).
I wrote a partial script for checking radius a while ago, but it was for checking if cursor was inside of an object or characters radius. It could be modified for characters only, but I'm not sure how you would handle the events to be triggered after contact. Making the character or characters simply stop is simple, but you might want to have one of the characters veer off their current path to go above or below the other character then resume the path they were on, or you might want (like in lure of the temptress) your characters to stop & greet each other with a fixed or random message. I know off the top of my head how to do the stop method & I know how to do the talking one too, the one that involves the characters walking around the other one is a little complicated for my brain at the minute; besides: I've not had my weetabix
P.S: the chase feature you mentioned is essentially using the radius thing I mentioned, just it's done by the engine instead instead of a custom script.