With the number of reps you have in that plan (40), it looks like the goal is to get that burn/exhaustion in the muscle, and the cardio rate up.
So I would try doing 40 step-ups on the left, then 40 step-up’s on the right. The way they have it worded for the side step-ups makes me think that this is what they mean.
But when I personally do step-up’s as part of my warmup before climbing, I alternate feet. It makes for a slightly weird hop at the bottom, bc I step up/down with the right, switch foot, step up/down with the left, switch foot, etc. (I just do one of those tabada-style 30sec on/10 sec off 8 min workout thingies, and my goal is to warmup, to to get exhausted, lol).
In exercises like these I consider step left/step right to be a set of 1. So either way, whether you are alternating or repeating the same side, you will have a total of 40 on each side.