This definitely isn't a common phrase. "I am gamed out" would mean "I've played too many games today and I'm ready for a break" and you can "game the system," which could involve using strategy to make a social system play to your advantage, like using a tax loophole. So by extension if a person is "gamed" it might mean that they're being tricked or taken advantage of.

I highly recommend you to get to know Urban Dictionary dot com

>><a href="https://www.urbandictionary.com/define.php?term=I%27m%20game" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);">I'm game</a>

Used to <a href="https://www.urbandictionary.com/define.php?term=indicate" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);">indicate</a> that <a href="https://www.urbandictionary.com/define.php?term=the%20speaker" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);">the speaker</a> is interested in doing whatever has just been suggested. Similar to "<a href="https://www.urbandictionary.com/define.php?term=I%27m%20up" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);">I'm up</a> for that."

<a href="https://www.urbandictionary.com/define.php?term=Bart" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);"><em>Bart</em></a><em>: Let's go see </em><a href="https://www.urbandictionary.com/define.php?term=a%20flick" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);"><em>a flick</em></a><em>.</em>

<a href="https://www.urbandictionary.com/define.php?term=Lisa" rel="noopener noreferrer" target="_blank" style="color: rgb(19, 79, 230);"><em>Lisa</em></a><em>: Sure, I'm game.</em>