It is true that either would be grammatically acceptable ("It was eerie to be standing ..." or "It was eerie to stand ..."). I think you recognize that, and are asking about the difference.
I would say it is mostly a choice of style, in this case. The two statements could be read as exactly equivalent. So, the simple answer is that the author thinks "... to be standing ..." simply sounds better. This could be the entire answer.
To dig a little deeper, and probably confuse things in the process, 'eerie' describes the verb. In one case the verb is 'be'; 'standing' describes how he is being (in what state he exists), and 'eerie' describes his feeling about that (about 'being', and about the whole clause, 'being standing').
In the other case the verb would be 'stand'. So, a difference is that it is not specifically the act of standing that is eerie, it is the state of being. He would feel equally ill-at-ease sitting in front of them, with everyone waiting. It is the being in front of them, with them waiting, that is eerie - not what state he's in while he's there.
Another note is that 'standing' means 'being still' (like 'standing water'). 'Sitting' actually works for this, too (like a 'sitting duck'). (Although you can use them as opposed action verbs - "It is exhausting sitting down and standing back up all day" - in which case you are neither 'sitting still', nor 'standing still').