That convention makes states (i.e. national governments) liable, but doesn't by itself make SpaceX liable. I assume SpaceX would be liable under ordinary tort law in the U.S., irrespective of the convention. At least for claims against U.S. nationals, the convention is probably mostly irrelevant; it's purpose is to act as a backstop in case compensation can't be found using normal legal procedures--e.g. courts won't otherwise hear a claim (AFAIU, the U.S. is relatively liberal in permitting foreign entities to sue in domestic courts for all manner of situations, and to do so on equal footing), or the entity is unable to pay compensation, in which cases the state signatory effectively acts as a guarantor for all the entities within its jurisdiction.

> That convention makes states (i.e. national governments) liable, but doesn't by itself make SpaceX liable.

The US is liable for any damage from space SpaceX causes in a different country. If it hits a house in the US, that's a completely different question.