When someone gets caught on terrain, their movement is interrupted and there is idle time before they retask to moving again. This is explicitly how I've managed to survive chases before, the pursuer got stuck and had to navigate around an obstacle they only ran into because they were following the shortest path and there was something in the way that I had already gone around.
I've already said this a few ways, I'll try one more. It is not a problem if it's theoretically impossible, in an idealized situation, for the pursuer to win a chase. It's OK if in that scenario the chase extends forever. There is no reason that winning a chase needs to be the default position and I would argue that the opposite would be better for the game, at least so long as it's not possible to abuse this to engage in constant harassment. I think it's better for players to be rewarded for using tactics to catch their targets rather than pure aggression.
Speed boosts were not in the game last time I played. They give a small advantage to someone who's trying to escape if they step on the right tile, but they give the advantage to the pursuer if the pursued miss them. Sometimes. Other times, the speed boost is far enough out of the way that taking a detour to step on it would not be worth the displacement or lost stamina. (Even if some clients do help with this, they can't make you go for the speed boost all the time or sometimes they'd just be frustrating and counterproductive to use.)
When I say someone that wants to catch up has to be smart, I mean they have to actually outthink the one they're pursuing. Predict where they'll go, flush them into an ambush, feign defeat and then ambush them while they're recovering, ambush them in a location where they have nowhere to run, or any of a million other potential strategies other than "run faster". There are players to whom that isn't a fantasy land, it's the normal way they play.