I certainly didn't mean to imply that a nurse's response would be:
"Gee, the guy is having trouble breathing".
I've worked in NZ, Aus and UK, and in those countries only nurse practitioners are trained to make complex diagnoses. Nurse practitioners make up a very small portion of registered nurses, and I think it's important to make this distinction so that the OP can make the scenario more realistic (as I think that's the goal the OP has in mind). I still think it would be fair to say that a nurse without advanced training (i.e. without a nurse practitioner qualification with a focus on emergency medicine) would have difficulty making that diagnosis. As would a primary care/family doctor, paediatrician etc. as they simply don't have the training.
Excluding nurse practitioners, one of the defining differences between a nurse and a doctor is the formulation of a diagnosis, no? There are certain differences between the two professions that are complimentary. For example, doctors have no idea how to draw up and administer medicines because it's not part of their training. I don't think that's an old-fashioned idea - it's the reason we have the two professions. I would love to know if you think I'm wrong about this though!
That aside, the question here was regarding a tension pneumothorax, specifically, which can be a difficult diagnosis to make even in a well-equipped emergency department setting. So, I think making it on a sidewalk would be hard.
PS that list is super-vague. A tension PTx would come in under the "mode of breathing ineffective" umbrella but I've never heard it described that way. The issue in a tension PTx is that air can enter the hemithorax but can't exit. So you get a mass effect, compressing the great vessels leading to cardiorespiratory compromise.
What country are you in?
Technically neither a nurse nor a doctor could make that diagnosis without an X-ray or tapping the pleural space to see if blood or air were there. Both professions are capable of suspecting a deflated lung on one side.
In the US nurses diagnose a lot of things. In this case we look at a different aspect but one doesn't just say, "Gee, the guy is having trouble breathing". You would note air was only going in one lung. Once that is determined there are only a couple things that would cause it.
Nanda Nursing Diagnosis List
Sorry, I get my hackles up when people have old fashioned ideas about nursing.