Hang on now.
We're just saying, "Oh, the hero has more hax. He wins."
Game Super Sonic having a "cool head" means nothing here since he's bloodlusted. And Fleetway Super Sonic is always bloodlusted because that's in-character for him. Honestly, I see Fleetway Super Sonic going in for the kill way before Game Super Sonic.
Also, all of Sonic's powers that actually mean something--the Color Powers--are strict time limits, and can only be used one-by-one. It's also pretty easy to deduce what they do (Red Burst makes him a giant fireball, so he's hot), which puts him at a severe disadvantage. Furthermore, he has nothing to counter Fleetway's intangibility that's granted to him simply by going fast. Game would literally need to stop Fleetway from moving, and I doubt he'd figure that out, because... honestly? There's no way to figure that out! Being bloodlusted, he's not going to think about strategies. Meanwhile, Fleetway can get to Game just fine. And then just turn him into an electron bomb, or turn Game into a pile of molecules. Matter manipulation bypasses conventional durability, so it doesn't matter if Game is more durable. Which he likely isn't, honestly. Solaris being superior to something that stabilizes two universes, and then destroying some timelines is mentioned, and Game needed the help of two others. Even then, they still couldn't permanently defeat such a force. Meanwhile, Fleetway is massively superior to someone who was fiddling with several universes for fu. God Robotnik wasn't exerting himself in the slightest. So really, the two are closer than one would think. And even then, Fleetway has some regen and intangibility to make up for any A.P. advantage Game has.
Next, Super Sonic's most useful abilities--manipulating time, using Chaos Control and such--won't work, since Fleetway resists time manipulation. Honestly, when angered, Game goes for those types of techniques, so he's only setting himself up to be skewered by Fleetway the second he sees it isn't working for some odd reason.
In the end, Game has more hax, but the useful bits are either on-timer, not passive, or Fleetway resists. Meanwhile, the two shouldn't be too far apart in stats, and Fleetway has two things that Game cannot counter; passive intangibility simply by going fast, and matter manipulation. Since both are bloodlusted (one in this situation and one naturally), they'd both go for their ace-in-the-holes. Game would see his powers don't work, and would then get turned into a pile of molecules.
Fleetway Super Sonic should win this, and handily.