the problem with all these unorthodox methods is they hardly work for most situations, you'd be better off using waypoints or grids.
For a simple chase A.I. you could log the players coordinates at a certain rate and make the computer follow these coordinates... kinda like you making tracks in the snow and someone chasing you using your tracks as a guide.
The problem though is if you don't sample the coordinates fast enough you could end up with the same problem as:
in this case, the sample rate is high and the enemy could easily follow the logged coordinates "o" of the player around the wall "---"
o...o...o...o...o..
----------------- o
............o...o.....
in this case the sample rate is low and the enemy hit's the wall trying to get from the 3rd corrdinate to the 4th.
o.......o.......o...
----------------- .
.............o........