I can only speculate, why this variant is common in german but not in english. But I can explain the grammatical structure:
The singular indicates that "Rang" is referring on the indivdual rank of each person. So a literal translation (which sounds a bit odd in english) would be
Two people with different rank each.
I think - but this is speculation - the preference for Singular in this case is caused by the idiomatic phrase "von Rang" which is often used in singular, like in "ein Offizier von Rang (meaning 'an officer of high grade'). Another example is "aus dem Hause". It would be possible to hear the phrase
Zwei Prinzen aus unterschiedlichem Hause.
But, as a tertium comparationis, consider
Zwei Menschen aus unterschiedlichen Familien.
Zwei Menschen aus unterschiedlichen Städten.
where it would be very uncommon (if not wrong) to use the Singular, because no such idiomatic phrase for singular exists. These exmaples lead me to my hypothesis, that the Singular is caused by the idiomatic fixed phrase "Mensch von Rang".
This is also supported by the fact that
Zwei Menschen von unterschiedlichen Rängen
can also be translated as
*Two people from different balconies
since "Rang" also has the meaning of 'balcony' (in theatre or opera). This latter meaning is excluded by using the Singular, because for this meaning it would be obligate to use Plural - again, because the idiomatic singular phrase does not exist for the meaning 'balcony'.