Thanks, Colonialist. May I suggest for the first one, a combination of your two: “He glanced back down the street,” as the “back” assumes they came that way, and is more concise than your second one. Thanks for dropping by and commenting! There’s certainly no “correct” answer to any of these, but actions scenes demand brevity and to-the-point phrasing.

Kassandra, for jumping in with your solutions, I’ll send you a free PDF of my latest e-book, Style that Sizzles & Pacing for Power. You can claim your prize by emailing me at j.renner.editing@hotmail.com.

Love your solutions, Will! If you contact me at j.renner.editing@hotmail.com, I’ll send you a free PDF of my latest e-book, Style that Sizzles & Pacing for Power.

My attempt:
He looked quickly down the narrow street in the direction they had come.
—He glanced back down the street.

As soon as Chris started to rise, Nathan saw it as an indication he was going to follow, and started off back in the direction of the elevator, this time worrying less about his silence and more about haste.
—Chris stood as if to follow, so Nathan set off towards the elevator. Speed was more important than silence.

—Will’m

Thanks, Lauren!

Thanks for dropping by and leaving a comment, Andrew. Yes, those insignificant details not only slow down the pace, but they can be like little bumps in the road for the readers, jolting them out of the story momentarily.
I think it’s important to show the POV character’s reactions, however fleeting, as in a flash of pain or other visceral reaction, or a quick decision to change course in some way, as, unlike a movie, in a novel we’re in somebody’s head, usually the protagonist’s, and feeling their reactions brings them to life for us and makes us more emotionally engaged in their plight, rooting all the harder for them.