Yes "random walk" is not a strategy, it is a model. This article basically just says:"Jumping bean motion can be modeled with random walk", which isn't really suprising.
Maybe the name of the strategy should be "directed random walk".
I.e., it's a strategy at the species scale, but not the individual scale.
But, maybe that's my mistake of not knowing how these words are used in biology.
Point being, I wouldn't worry too much about "having a strategy" vs. "natural selection selecting for". It's only ever the latter - perhaps with exception of humans, but that's up to philosophers to figure out.
I think it's mainly the ability to start or stop jumping according to temperature. Jumping in a random direction, only when you're too hot, is a strategy for finding shade. Given a pattern of light and shade, that strategy is provably better than never jumping at all, or jumping regardless of temperature. (I haven't proved it, but I think I could.)
I think they're saying a jumping bean "has a strategy" in the same sense that a Roomba "has a strategy." The Roomba has an edge over a traditional vacuum cleaner. But if it's you against the Roomba, you're normally going to win.
it seems like the bugs have only one motor function - move in a random direction - and only one input sensor - temperature. What other strategies are available to them than random walk with a probability of movement based on a function of temperature and time?
If the bugs had the functions 1) move in one direction and 2) turn, then they might have observed a circular or spiral path.
First, they have no evidence that evolution could create a jumping bean that jumps in a straight line. It seems that the direction the bean moves is a function of the uncurling larvae but also the shape of the bean. Possibly such a movement could have evolved, but the authors are presenting this like the random walk improved the larvae's fitness function.
Second, the conclusion that a straight line would find shade quickest, but only for a small percentage of larvae, is obvious and doesn't result in anything scientifically new. Of course if you draw straight lines from any point in all direction, the straight lines that happened to intersect with the shade will be the fastest path to the shade. But just as obviously, heading in a straight line in a random direction is not the most efficient way to find shade.
If they had the freedom to evolve any search strategy possible, there are plenty of search strategies that will uncover shade faster than a random walk. But the larva don't have the ability to select any search strategy they want, they're blind and have no senses besides their current temperature. They have no way of knowing which direction they're facing. Therefore a random walk is simply all that is available to them, it's not a strategy.
Given zero information about your surroundings other then the fact of whether you are currently in a shade or currently not in a shade traveling in a straight line is a mathematically better strategy.
Why? Because random walk includes the possibility of going back to the same place of where there is no shade while traveling in a straight line guarantees every move is a new location.