Is the phrase order in this sentence correct?
It is not odd.

项目 is the subject of 起源 (and cannot be used an object), but the object of 推广 (and probably cannot be used as subject).

We can say 项目推广, but this is used as noun phrase which means the "the promotion of the event". It is like a short form of 项目的推广, where 推广 is a noun.

"现代五项这个项目最早在哪个国家推广的？" This may be treated as implicit passive voice, "现代五项这个项目最早在哪个国家（被）推广的？"