Your OP is correct except there is a train that can take you between the DL and EK terminals.
https://www.fly2houston.com/iah/inte...transportation
But because we'll have bags, we'll have to collect them from domestic baggage claim and then transfer over to the international terminal to check-in and check bags with EK. The train seems to be airside, so I'm more wondering how we get to the other terminal landside.