I've got a '09 Tahoe, and bought that body-style Escalade's chrome door trim to put on my truck. Yes, the Escalade trim had tabs on the back, and the tabs went into holes in the Escalade doors, but the tabs were just plastic and can be clipped off. The tabs were only to easily locate the trim on the doors, and otherwise provided no mounting value. The trim stuck on with 3M tape. That's it.
If the new trim is anything like that trim, then just clip the tabs off the back and stick the trim on your truck.