The Lake Kindred game isn't just for the event, they're using this as a launching event for the game.
So any kindreds you catch/buy/etc. stay with your account as a playable item for the Lake Kindred game.
So you cant really equip it, but it stays in your inventory and you use it in the game. They just mean it's only here in the shop during the current event (which I believe lasts 30 days) and then leaves the shop, but you can still use it as a playable Kindred.