Basically we are generating a tame/wild "kangaroo" pair, which is actually just two sets of starting points. The starting point will be different depending on whether the kangaroo is labeled "wild" or "tame".
Then add [this is point addition we're talking here] slightly different incremental terms (mod the secp256k1 group order) until they either equal each other or we have added so much term value that it exceeds the search interval.
i.e if the interval is 2^40 we can only point add that much to the starting point before we have to discard the pair and start with a new one.
To speed things up we start hundreds of kangaroo pairs in parallel and see if any wild kangaroo equals any any tame kangaroo.
This program only stores the x coordinate of points do it might look like it's just storing and adding numbers, but actually the y point is computed from the x point so it's a compact way of storing points.