"I am standing and waiting by the gate" is a much more natural translation IMO - it's weird to split up gerunds that share the same helping verb.
Could it be especially because of the "and" in the sentence? Without it, it does not sound bad to me.
Or would you say that changes the meaning?
"I am standing at the gate waiting."
"I'm just sitting here watching the wheels go round and round...".
I think it's more natural to split them up, because I'm both "standing by the gate" and "waiting".
Your sentence implies that I'm both "standing by the gate" and "waiting by the gate", but the second seems overly precise.
The most natural English translation is "I am standing waiting at the gate".
I stay and wait by the gate?