Memory game - short or long-term memory?
Short-term memory capacity is very limited (How much can users hold in their short term memory), and that seems to be a fundamental property of short-term memory (Can working memory actually be improved?). So the longer this game progressed, the less likely it would be that players could keep the information in short-term memory. A few items would be fine. Ten items would be difficult, and items would start to drop out of short-term memory.
Memory experts use techniques like the method of loci to associate new information with an existing structure held in long-term memory. So they would have a significant advantage in this game.