Search algorithms have long underpinned game-playing artificial intelligence, however as game domains expanded from small deterministic board games to large scale, partially observable, real-time environments, no survey has systematically organized this evolving literature into a unified taxonomy or evaluated algorithms through a consistent design space. This taxonomy based survey addresses that gap through domain-scoped literature clustering, analyzing 61 works from 1946 to 2025 across six thematic clusters: spatial pathfinding and navigation, adversarial game tree search, Monte Carlo tree search and bandit based planning, metaheuristic optimization, learning augmented search, and search under uncertainty and partial observability. A four dimensional design space — covering interaction topology, information structure, computational regime, and source of search guidance enables consistent cross-cluster comparison of hybrid approaches. Analysis reveals a paradigm shift from analytic correctness and proof driven evaluation toward empirical benchmarking, sampling based planning, and neural guided search. Cross-cluster synthesis identifies fundamental tensions among decision quality, formal guarantees, and resilience under uncertainty, and documents an evolution in evaluation methodology from deterministic metrics to distributional robustness testing. Open challenges are identified, pointing toward principled frameworks for managing trade offs among quality, optimality, and robustness. This survey provides artificial intelligence researchers and game developers with a structured reference for selecting and evaluating gaming search algorithms across diverse environments.