My guess would be they steam it, then sauce it. When I make steamed broccoli I steam it over water until it's just about to my desired tenderness, then shock it in ice water.
Meantime, I sautee some chopped garlic in olive oil (just a minute or so, to cook off the "raw" taste), and then toss in the broccoli for a couple of quick tosses. Usually I add some crushed red pepper, and of course season everything. I would guess at this point you could just add some teriyaki sauce to the skillet, toss everything, and serve.