Does being on Earth count as being in space since the Earth is in space?
No. Technically speaking, the concept of space is better defined as "the vacuum of space".
It requires extreme force, strong seals, and strong walls, to create a near-vacuum on Earth. The moment the seals are broken, air INSTANTLY rushes in to fill the void.
If you place a glass of water in a vacuum chamber and turn on the pump, removing MOST of the air to create a near-vacuum effect (a true vacuum does not ever exist), the water almost instantly boils, without getting hot. A spin-dryer works by drawing the moisture out of wet clothes and is sped up by applying hot air to it.
These basic facts of physics alone prove that Earth is neither a spinning ball covered 80% with water under the relentless heat of the sun, nor surrounded by a vacuum. Therefore, we can safely say that the concept of "outer space" is actually relegated to the realms of science-fiction and Hollywood fantasy.
The fact we have an atmosphere at all suggests it is contained in some way, most likely in a similar way to how water is contained beneath its own level naturally.
It may even be that it's more like an impenetrable "firmament". If you consider the case of the deep-sea explorers in their pressurised submarine who discovered a bizarre "underwater lake", which resembled a normal lake that we ordinarily see above the ocean, not at the bottom of it. They claimed that when they attempted to descend into it, they bounced off, sending ripples like a skipping-stone across a flat lake.
With some evidence of people filming what's come to be called "the lunar wave" while filming the moon, it's possible that this "ripple" is a similar sort of phenomenon passing in front of the moon, across our firmament.
If in fact outer-space was a vacuum, we would lose our atmosphere with violent force immediately, all our water would boil, and this spinning ball would resemble the surface of the moon. Fortunately for us, Earth is beautifully designed, infinitely flat, and stationary.