This is a reference to the character's original – and still most commonly used – Japanese name of Dr Eggman. Talking of Dr Robotnik, Sonic taunts him by calling him 'Eggman' because Sonic thinks Dr Robotnik's army of drones look like 'flying eggs'. His home is attacked by a tribe of animals that look a lot like the Knuckles Clan that could lead to a Knuckles appearance in the sequel. There is also a nod to the other major Sonic character Knuckles in an early scene that's set on Sonic's home planet.
The biggest bits of fan service come in the credits scenes with Dr Robotnik sporting a look more in line with the video games in the first scene, while the second credits scene has a surprise Tails appearance setting up the sequel.