McDonnell Douglas F-15 Eagle (52-8088)

That almost looks like he has one engine shut down

On the other hand, he's also pushing in left rudder. Do the engines on the F-15 aid in rudder authority?

I think it's flying only by the right engine.

Left engine is at max thrust prior to augmenter ignition. Think of it like putting your thumb over the end of a water hose. The water pushes out faster. Same principle. Looks like the pilot missed the left throttle when moving to augment.