I think it's good to have the official context from the state of NY as well, which argues that Kalshi meets the state's standards for gambling; has serially refused to get the required licenses, and serves customers aged 18-20 in a market where gambling is restricted by law to people over 21.
https://ag.ny.gov/press-release/2026/governor-hochul-and-att...
My impression was that NY wanted a TRO to stop Kalshi operating in New York, not nationally. A TRO seems like a rather extreme measure in that it assumes the plaintiffs win the lawsuit as a premise, but I guess that's partly a function of how long New York has been trying and failing to obtain compliance with its gaming laws, and intended to provoke a preliminary hearing into the merits of the case (vs letting the litigation drag on for years without anyhting changing).
NY let DraftKings plaster Penn station and subway fare gates with ads before sports betting was legal there. They never sought an injunction to shut down those operations outside NY.