I suspect it took mouse events, and initially drew straight lines between them. That's necessary on 1990's hardware because drawing straight lines is fast, and you need to do it fast.

Then, when you are done drawing, it redraws the line, using the same points as before, but this time as input to a spline curve algorithm.

Drawing splines isn't much harder computationally, but notably if you add one more point to the end of a spline curve, then part of the line that you have already drawn changes. That in itself is very computationally heavy, since everything behind that line now needs to be redrawn - certainly not something you can be sure can be done at 60 fps!