Is everyone who worships the Greek gods today a practitioner of Hellenismos or a Reconstructionist?
No, absolutely not. Hellenismos is a specific religion based not only on the worship of the Greek Gods, but is based on the history, character, thought, culture, and ethical system of ancient Greece. Ancient Greece is the foundation of the religion. Hellenismos is not simply the worship of the ancient Greek Gods, using their names for the names of the Goddess and God of Neopagan religions, or injecting them into some magical system. This does not imply that there is a single, uniform theology, but it does state that we all draw from the same information. It also means that we do not eclectically blend religious practices and concepts together with the expectation of it still being Hellenismos.