They describe a leaderboard built from server members' shared gaming activity, while actual rollout remains unconfirmed.
When It Appears
“Last played {gameName}” can appear on a server view that ranks shared gaming activity and shows a timed competition when Discord displays the name of the game a member played most recently.
What It Means
When “Last played {gameName}” is shown, the current step is presenting the name of the game a member played most recently.
A user who saw “Last played {gameName}” in Discord is likely searching to confirm that it means the name of the game a member played most recently, where it appears, and which state it describes.