Isn't alpha-beta pruning a type of optimization you can do to a search algorithm, but not the base algorithm itself? I only bring this up since I helped make an Othello bot that used Mini-max _with_ alpha-beta pruning to help reduce the number of branches it needed to follow down a tree.
Alpha-Beta pruning is, to my knowledge, only really defined in a mini-max setup. By definition, it leverages the mini-max framework to prune areas of the search space.
You can apply the core concept -- refusing to expend computation effort when the result of that effort is guaranteed to not be used -- to any number of other methods and approaches in Machine Learning and AI.
As far as the first line in the wikipedia page goes..."Alpha-beta pruning is a search algorithm which seeks to reduce the number of nodes that are evaluated by the minimax algorithm in its search tree."[1] it seems like you're correct. Thanks.