First of all, she's not necessarily my dream girl, but if I was to have one, it'd be her. You know what I mean... everyone has one. Spoke to her briefly twice nearly a year ago, and I guess she'd be one of the girls, that at the back of your mind you'd like to keep that option open with.

She seemed a bit giddy and she looked better than ever. I actually thought it was quite sexy to be reminded of the fact that she can just go out and pick up studs as she wishes. And I didn't really mind it at all. But what I didn't like was the fact that I was there at the time. I'd actually went out for a walk. I was walking along the side-walk towards them(obviously looking at her ass, etc), and as she looked to the side as entering the door. I looked away at the last moment as I didn't just want to be seen as staring at them.

Later I kind of thought to myself, that looking away kind of seemed like submitting. It was almost as if I did it so she wouldn't feel slut shamed. Perhaps I should have just kept looking straight ahead and stared at her acting as though I've every much of a right to be there as she does.

Obviously everyone has both a certain amount of luckiness & unluckiness in their lives. So perhaps the fact that I was just the nobody returning home alone at the moment when she was heading up to have some great sex, didn't exactly do me any favors. Does the fact that I was there, make her subconsciously less inclined to associate me with sex, or feel as though this guy somehow triumphed over me.

Generally speaking though, did it ever happen to you, where by coincidence you end up in the proximity of a pretty girl and a stud(whom you might think you're as cool as) who are flirting or about to get down to business, and you end up saying to yourself "if I was better/smarter, I wouldn't be in this situation", but yet can't quite put your finger on it. Think of some cool player figure you know, and try to imagine them as the third person!

I suppose the only thing for me to glean is that most people my age don't "go for walks", or at least not at 1 o clock in the morning.

I imagine this is your main question. If I'm wrong tell me.
I have to say in advance that I was never in that situation, but I assisted already to other guys K-closing with girls I wanted, so I may be able to give you a quick answer.

Were you and the guy both trying to game her at the same time? Cause then she will see you as the one you lost and will associate you to a beta, because the other one won and is therefore more alpha than you. If you weren't, I don't see any problems. You were just walking to your place or one of you FBs' place to have sex for what she knows.
I would say that yes, it did lower you a bit from her point of view, but it's something that can be easily forget so you shouldn't worry about it.

Try not to talk yourself out of things you want to do before you do them. Why don't you just give talking to this girl a try before you defeat yourself in your own mind before you even try. Do something reckless that you are not comfortable with, push yourself to talk to her since it's obviously something you want to do. Even if you're just only saying hi awkwardly and that's all you manage it's better then nothing, just try, you obviously want to, just do it.