The minimum requirement for a state is a judicature made enforceable by military or police. So, some segment of your population is going to militarize, and the rest are going to either support or non-violently resist them. This would also imply the ability also to successfully grant amnesty or sanctuary to an immigrant or refugee, (requiring an extradition treaty) or otherwise resist the infraction of another state's law enforcement. A distinction should be made between a public body made sovereign by geographically or obfuscation, and a true state. Anarchy, for example, is not simply a 'state of no state'. Neither could the Caribbean pirate coves of the pre-revolutionary Americas, or some simple, self-organized collective. A true state is the direct imposition of, or relief from, regulations and rights by force.
You expose the subtly of semantics: how does the corporate charter differ from a state's statute; the executive board a government; the security branch a police force? Traditionally, the distinction was made by the corporation's reliance on a state's ability to enforce law, however the advent of PMC blurs even this. De facto, your SpaceX Hotel is already a state, a vassalage of the federal reserve, a subject of the world bank. To be truly sovereign, de facto à jure, you would need to explain why these semantics become relevant enough to require legal clarification. Was there a collapse of world markets? Are the world markets too competitive? Did a world-spanning conglomerate coerce the world's population into a robot-controlled dub-step party? A state can enforce its own markets and exchanges, and this would be a likely reason only if there exists a tangible, liquidable intensive to divorce from the current corporate scheme. And don't ignore the scorn and reprisal of creditors whose investment you've absolved by rebelling, unless you're willing to grant them a position of rank in this bright, new future.
I can see two extreme cases between which this future is possible. First, if the space hotel proves a bad investment, goes bankrupt, and is abandoned by anybody on earth who would otherwise care about the (organized?) bunch of radical squatters spouting nonsense about sovereignty and self-determination and whatnot. Unassuming, at first, they produce a vivid art and culture capable of projecting their desires upon future generations, and, thus, earning itself a place of distinction (even if only footnoted) in the history books. The alternative is a venture so massively successful they dominate the space market and buy out large portions of related industry sectors. Here, they are likely to encounter resistance from other, competing corporations, irk the ire of regulatory organizations, and conflict with anti-trust and monopoly laws of several countries. Statehood, than, would be a defense measure, the central corporation would 'evolve' into a government, and all the subsidiaries become separable corporate entities protected within. This 'evolution' is not a 'revolution', as the sheer infeasibility of space combat validates will without force or threat of reprisal.
Either way, their message to earth would be something like, “We don't need you. We are free. Deal with it.”