I rewatched the trailer a couple of times. Actually, there's no telling that Robotnik/Eggman has already taken over. In SatAM he has rebuilt Robotropolis how he sees fit. However in the trailer we see a city in ruins, on fire. The city itself looks normal, not like it's been under Robotnik/Eggman's reconstruction. He wouldn't destroy his own city unless it's a collateral damage in battle with Sonic. However Sonic stands in the distance and rushes in to stop the giant bots.Taking this into consideration, I assume the giant bots in the distance attack the city itself, the civilians and any military force if there is one. That means that either Robotnik/Eggman only tries to take over the city (which not necessarily equals "the world" in the setting) or it could be merely a ploy to draw Sonic's attention. The resistance, that was mentioned in the trailer, might suggest an uphill battle with Robotnik/Eggman, who has either built a new advanced army of robots or has obtained a new source of power or joined forces with someone powerful or even just had enough time to build a lot of robots to get the upper hand by numbers.
The setting might be a peaceful kingdom that lived in prosperity until R/E came. The resistance might mean the random bold citizens of the city under siege that decided to fight R/E with Sonic, which serve just as quest hub/base filler, where you hang out between stages/missions and have story dialogs or whatnot.
OR it could mean what we immediately assumed - R/E has really taken over and as an unstoppable force is crushing the few remaining cities. Thus, not able to stop him outright, Sonic and the team (whoever that is) tries to gradually whittle down his empire and gather enough power/artifacts/chaos emeralds to engage in the final battle.