Internet communications which exit/enter the state do, but there's still the issue of communications which stay within the state. The states have Congress-given authority to regulate intrastate (not interstate) internet communications. Moreover, by reclassifying broadband from Title II to Title I, the FCC gave up the part of its authority that allowed it to preempt state net neutrality laws. I wrote more on this technicality in a different comment [1].
Even when conduct could Constitutionally be regulated by the federal government under the Commerce Clause, that doesn't preclude state regulation unless Congress has (1) specificallly regulated that states may not regulate, or (2) has regulated in a way which the State regulations at issue would fundamentally conflict with.
So, yes, the internet is Constititionally a thing the federal government can regulate, but that doesn't make it Constitutionally a thing state governments can not regulate.
I can live in California and visit a site in California and my traffic might not leave the state. That is pretty much irrelevant now that Wickard v. Filburn is a thing though.
[1] https://news.ycombinator.com/item?id=37946794