Building AI Scientist agents with Large Language Models (LLMs) has recently attracted growing attention. Since scientific discovery fundamentally relies on uncovering causal relationships from observations, the capability of causal thinking, i.e., distinguishing causation from correlation and recognizing hidden biases, is essential to LLM agents. Although a number of benchmarks exist for AI Scientists, none explicitly incorporate challenges from selection bias, measurement error, and hidden confounders that widely exist in real-world scientific discovery. To this end, we present CausalGame, a benchmark that evaluates the causal thinking capabilities of LLM agents through interactive games. CausalGame asks LLM agents to actively design experimental protocols, collect observation data, and derive a final solution with an explanation report. To emulate realistic scientific discovery challenges, we design 14 scenarios that incorporate selection bias, measurement error, and hidden confounders. Across 30 LLM agents, none demonstrates reliable causal thinking: the best model reaches only 68.0% survival against analytical optima of 78-85%, and merely 5-7% of sessions receive credits on the causal-reasoning rubrics. CausalGame provides a scalable and controlled testbed for evaluating the causal thinking of AI Scientist agents.