I'd say this touches more on the mechanics of time travel than free will. So if this "predictor" is nothing more than a circuit that sends information to itsel

I'd say this touches more on the mechanics of time travel than free will. So if this "predictor" is nothing more than a circuit that sends information to itself in the past, there must be a "me" that pressed the button without seeing the light, before the data is transmitted to the past to the "me" that then sees the light but at that exact point splits off into a separate timeline. And then I would have free will again. Of course I am assuming time travel where travelling forward in your own timeline is impossible, something the article seem to not really go into.