Vortagots are definitely one of the list interesting Half-Life creatures. He broke the fourth wall twice in this area. "Far distance eyes look out through ours" Refers to the player looking through Freeman's eyes. "Something secret steers us both. We shall not name it." I believe could be referring to the player controlling the game, or the code controlling everything.
I was invested in the story and thought about G-Man as the eyes looking through Gordon's, then your comment took all the magic away. Now I realise G-Man's employers who need Gordon whenever they make a new game are Valve 😢
"how many are there in you? whose hopes and dreams do you encompass?" hes talking about how many players there are. hundreds of thousands of people look through freeman's eyes.