Video games feature a dynamic environment where locations of objects (e.g., characters, equipment, weapons, vehicles etc.) frequently change within the game world. Although searching for relevant nearby objects in such a dynamic setting is a fundamental operation, this problem has received little research attention. In this paper, we propose a simple lightweight index, called Grid Tree, to store objects and their associated textual data. Our index can be efficiently updated with the underlying updates such as object movements, and supports a variety of object search queries, including k nearest neighbors (returning the k closest objects), keyword k nearest neighbors (returning the k closest objects that satisfy query keywords), and several other variants. Our extensive experimental study, conducted on standard game maps benchmarks and real-world keywords, demonstrates that our approach has up to 2 orders of magnitude faster update times for moving objects compared to state-of-the-art approaches such as navigation mesh and IR-tree. At the same time, query performance of our approach is similar to or better than that of IR-tree and up to two orders of magnitude faster than the other competitor.