It's the Barrel of Doom!
This mug counts as something "Secretly Sonic". Only a true fan could recognize what this mug is here to represent. It's the spinning barrel from the Casino zone in Sonic 3. The zone had several of these barrel shaped items, and they could be found moving up and down on their own, moving side to side, or, static. Most of them were used as lifts/traps etc. in the level. However, there was a choke-point in the level.

ALL paths through the level worked their way to a single choke point that had a barrel in it. Jumping on the barrel caused it to dip down, and then spring back up. It BLOCKED the way to the end entirely. However, no-matter how much or how well timed one was to jump upon the barrel, it would never propel down far enough to allow a character out through the bottom of the choke point.
REMEMBER:
The game was released BEFORE the internet. One could not simply look up a guide online, or ask friends what to do to pass the barrel. Something like this where the method is not obvious was a serious issue in the past. The actual method for passing it was to stand upon the barrel, still. Then, rythmically use up and down on the controller (without ever jumping) to have the character shift their 'weight' on it like you do on a swing-set. This would propel it down juuuuust enough to slip out at the bottom-most point in its journey.

This barrel issue stopped many, many players in their quest to beat the game, and stymied others for a long time. It's unknown whether the developers intended it to be such a problematic item or not. Maybe they thought players would stumble onto the up/down on an earlier barrel in the level.
So, the story of the barrel, as any classic fan could tell you inspires this mug to get made. It is in the SegaShop online in 2019 for about 15 dollars.