Would it not also be correct to say: taw retlhDaq QamtaH
Yes; that would be completely correct as well.
Using chaH might be used to indicate that it's they (and not he or she) who is standing there -- i.e. for disambiguation or perhaps for emphasis.
Adding chaH is not wrong, leaving it out is not wrong.
We sometimes include pronouns as subjects, sometimes leave them out, both for variety and to show that both possibilities are possible. (And sometimes to constrain the possible translations.)
Imagine that I said: tlhIngan legh 'e' nID qoq. taw retlhDaq QamtaH. ("The robot attempts to see the Klingon(s). He/she/it/they is/are standing next to the road.") It is not clear which is standing by the road (or even how many klingons there are).
taw retlhDaq QamtaH 'oH makes it clear we are talking about the robot.
taw retlhDaq QamtaH ghaH would make it clear that we are talking about one Klingon.
taw retlhDaq QamtaH chaH tells us that there are multiple klingons by the road.
The pronoun is not required, but it can often help to clarify and so you must learn how to both use it and interpret it. That being said, when doing the reverse translation exercise (translating the English sentence into Klingon) it is marked correct either with or without the pronoun.