No, putting “playing Age of Mythology” on your resume is a bad idea.
I disagree but you are entitled to your opinion.
No, he’s totally right. Unless that is somehow relevant to the job you’re applying for (which I very strongly doubt, even if you’re looking for a job in the video game industry), that’s something that would almost certainly make any HR manager throw your resume in the trash.
The only time I could see it being worth including on a resume is if you’re applying for a job QA testing real-time strategy games.