This is an actual construction method called concrete stamping. Its a lot cheaper than “pavers” or bricks, and when you’ve a large amount of ground to cover like a sidewalk that translates to substantial savings in construction costs.
The gaps are sealed so water runoff and algae are not substantial concerns; they just beed to be resealed evry few years. The pattern is for pure aesthetics, any benefits in terms of grip or thermal expansion/contraction is insignificant.
The downside to this method is that the “tiles” will crack eventually, and replacement of individual “tiles” is impossible without destroying a larger part of it. But if you’re ok with cracks, and for most sidewalks no one cares about cracks, then stamped concrete is an excellent alternative to pavers.