There are 64 steps on each side; 64 * 4 = 256 steps per lap.
I counted every tile that I walked on and triple-checked... I also accounted for the slow steps that you took in the sand dune tiles.
It also makes sense to have every side the same length because you're going in a straight line; if one side is 64 tiles long, the opposing side will be 64 tiles too, since you're turning at a 90 degree angle and driving around in either a rectangular or, in this case, a square shape. Unfortunately I didn't make that mathematical revelation until after I had counted all four sides, because I only really needed to count two sides...
Anyway, yeah. 256 steps per lap.
Hope I helped. :)
