Conventional chess programs use a similar algorithm and ones like AlphaZero are similar except they use machine learning and neural nets to judge how good positions are rather than a simple point score system.
I remember trying to write a similar one after seeing the algorithm explained on the TV show Tomorrow's World, around 1980. (Here they are explaining the cutting edge of mobile phones in the day https://www.youtube.com/watch?v=vix6TMnj9vY&feature=youtu.be...)
That's a strange statement. For one, because chess players are hardly judges of what is and what isn't AI.
Among chess programmers there may be such an opinion here and there, but originally chess was a classical AI topic and alpha/beta search a classical AI algorithm. As are neural networks and Monte Carlo tree search. So it's quite a strange opinion, IMO.
On the other hand, they happen to be great judges of human- vs engine- style of play. If you ask any of the top players who have spent time reviewing games by chess engines, I think you'll find a consensus around the belief that Alpha Zero and LCZero play far more human-like moves than do engines like Stockfish.
The traditional engine tends to be extremely conservative and materialistic, only playing a sacrifice when it has calculated a line which recovers the material with interest (or forces checkmate). The so-called AIs don't do this. You're far more likely to see them sacrifice material for a long-term positional advantage, like a great human player would.
From my experience looking at Alpha Zero and LCZero wins against Stockfish, one of the more common patterns I see is a sacrifice by the AI which gives such a dominant position that one or more of Stockfish's pieces become uselessly trapped behind their own pawns. It's this sort of position which seems perfectly tailored to exploit Stockfish's materialistic nature.
The original AlphaGo paper even mentioned that they tested the bare neural network predictions against the version with MCTS guided by the network and found that the MCTS version won 100% of the time, which strongly suggests that search is an indispensable part of strong AI performance in games.
Typically, chess engines are built on minimax, with optimizations like alpha beta pruning.