The complexity of computer games is ever increasing. In this setup, guiding an automated test algorithm to find a solution to solve a testing task in a game's huge interaction space is very challenging. Having a model of a system to automatically generate test cases would have a strong impact on the effectiveness and efficiency of the algorithm. However, manually constructing a model turns out to be expensive and time-consuming. In this study, we propose an online agent-based search approach to solve common testing tasks when testing computer games that also constructs a model of the system on-the-fly based on the given task, which is then exploited to solve the task. To demonstrate the efficiency of our approach, a case study is conducted using a game called Lab Recruits.