In this research, we use a process data analysis approach to gather additional evidence about students' argumentation skills beyond their performance scores in a computer-based assessment. This game-enhanced scenario-based assessment (named Seaball) included five activities that require students to demonstrate their argumentation skills within a scenario about whether junk food should be sold to students. Our research sample included 104 middle school students. Process data analyses focused on an "Interview" activity in which students explored different locations and interviewed various characters to identify their opinions on the junk food issue and categorize each opinion as pro or con. Students could take various paths to complete the activity. Results indicated that the number of trials students made in the Interview activity predicted their performance on the Interview activity as well as the total Seaball scores. It was also found that most students improved their answers in the Interview activity after receiving automated feedback and making corresponding changes. Besides the connections between student activities and performance, results from analyzing the process data helped us to identify difficult items in the task. We conclude with implications for conducting process data analysis to better assess students' argumentation skills and to inform task design.