The NYSE is only one of 11 registered US equity exchanges. There are other exchanges that open earlier and close later (for example the NYSE owned Arca exchange trades from 4am to 8pm Eastern).
Stocks in the United States generally aren't listed outside of NYSE and Nasdaq though (unless you count BATS).
It doesn't matter. You don't have to trade the stock at its listing exchange.
Generally that's true, unless it's an IPO, halted, suspended, sub-penny, etc...