Yes SpaceX's Raptor engines would be built in Hawthorne, CA and tested in McGregor, TX like the Merlin before it. But at Boca Chica, TX they are not just fitting the components into the an already completed fuselage, but welding the entire air frame together, including the pressure vessel bulkheads and stacking the stainless steel rings into Starship and Super Heavy. As far as I know Boca Chica receives stainless-steel sheet metal and turns it into the rings segments. The rings have a 9 meter diameter, so cross-country road transportation would be a problem.

The "massive" rocket he's referring to is Starship, multiple versions of which are being built in Texas, not Ca.

How much of it is actually built in Texas, vs just final integration? Does Boca Chica have its own engine assemblyline?

The engines are built in Hawthorne, CA before being shipped to McGregor, TX to be tested then are integrated into the final assembly in Boca Chica, TX. Every other part of the launch vehicle (besides avionics systems, also manufactured and tested in Hawthorne) is manufactured and welded on site.

By mass and size, Boca Chica produces the majority of the rocket. By cost and complexity - rocket engines (of Raptor kind) and control systems (of SpaceX kind - with all kinds of telemetry channels) win from Hawthorne.

Not the case, there are parts arriving in TX all the time. Downcomer being an example.

That said, what they are doing in Boca is clearly very impressive and its much more then just an integration facility.