In theory, she should be invoking the gods, and the talismans and such are just mediums for the gods to act through. Would that be magic? Iunno, magic's pretty ill-defined in Touhou. Is that for sure what Reimu's actually doing? Iunno, Reimu's pretty ill-defined.
She only invokes the Hakurei shrine god, who up till now has never been seen. Touhou doesn't have a defined magic system which is just fine, because it's all based on mythology and as far as the canon is concerned, all that matters is that all of it doesn't exist in the real world and so exists in GSK.
Zun is able to use this soft system because of Reimu herself. She can resolve every incident not just because she is the Hakurei Shrine maiden and has the abilities given by the aforementioned god, but because of her float ability, which in turn lets her use Fantasy Nature. Nothing can beat Fantasy Nature and it's related abilities, and the 'how' doesn't need to be explained since its a catch all.
That's fine for a game and a setting which is left for the community to make their own stories in. It's just an issue when Zun has to essentially establish canon interactions between people and abilities in actually fleshed-out written stories such as this. Does Marisa use the 'same' kind of magic? What is divine power? Are there other systems? Or is it all magic?
It's a lesser-known thing with Reimu that she claims none of her abilities are "magic", but divine intervention. But it contradicts the fact that her ability to float is innate to her and doesn't have to do with the Hakurei Shrine god. So is she lying or unaware of the details of her other abilities? I just wonder if Zun is referencing that here, because I certainly don't expect him to explain it. It's just an interesting topic.