Air target intention recognition (ATIR) is critical in the modern air defense operations. Through the analysis of typical air defense combat scenarios, first, the paper defines the intention space and intention parameters of air units based on military experience and domain knowledge. Then, a human rules-based game agent for online intention recognition is proposed, with no training, no tagging, no big data support, which is not only for intention recognition, parameters prediction, but for formation identification of air targets. The most critical point of the agent is the introduction and application of thermal distribution grid graph (TDGG) and virtual grid dictionary (VGD), where the former is used to identify the formation information of air targets, and the latter is used to optimize the storage space and simplify the access process for the large-scale and real-time combat information. Finally, to have a performance evaluation and application analysis for the algorithm, we carried out a data instance analysis of ATIR and an air defense warfare simulation experiment based on a Wargame platform, both of them verified the effectiveness, practicality and feasibility of the proposed game agent compared with the classical k-means and the sector-based forward search method.