what kind of property ?
As far as its oversight of the DNS root is concerned, IANA only controls the Internet to the extent anyone else wants to be listed in its directory and others want to continue using it in preference to some alternative root. The root zone is a small file and anyone who wants to, and has the infrastructure ( a few powerful enough servers in secure hosting on different continents will do) can replicate and serve it to whoever wants to ask them for it. The last point is made slightly more complex with DNSSEC, but only to the extent of needing to patch operating systems to accept a different root zone provider trust certificate as valid.
Having a private "non profit" registered in California do this job seems a bit weird and corruption inducing, and so is FIFA. The alternative is the relative legitimacy (in relation to international law), glacial responsiveness and byzantine bureaucracy of the ITU which has similar oversight of the global dialup phone system.