Yes it does.  It's the possessive form of thou.

Okay, lets break it down

Its like forgetting about everything
Its like, staring at the sky

The theme is despair. Someone who is despair would lack hope so that person would stare into the and forget about everything and just give up.

Or as deception always find a way
Like forgetting about a friend

When I wrote this years back I'm sure this part was about someone, but those who decieve, become victims of their own actions, and use people instead of make friends

As lying got the best part of thy
Its like lying to yourself

Once a lyer, always a lyer. One who starts to make lying part of their personality will start to believe their own lies.

For when it starts early its too late
Like a poison from a snake

If a parent teaches their child to be racist, to be judgmental, to be mean, etc. most likely they will remain so . . .

 
Thy never kept an open mind
Like those without friends

Listen to new theories, try something new, be different, move on for once, then you may be appealing to more people . . .

Always disrespect to never listen
Like a bond looks not it is

Just because that guy is still with that girl, just because he is still in good relation with his mom, doesn't mean their is a bond, sometimes relationships between people are bad because one person will not respect or appreciate the other . . .

 
And those things that thy have stolen
Like a thief who shows guilt without words

Sometimes one can tell who did it without the one who is guilty having to confess just by reading them, facial expressions, mood, the way they sound etc.

Thy greedy demon manipulates
Like you know so well but cannot trust

If you ever suspect something, and get that feeling, then you start to loose trust . . .

Confessing never was thy cup of tea
Like a demon child which parents no control of

The first step to recovery is admitting the problem. If a child is a bad child and the parents won't admit it, they won't do anything about it . . .

Living a life on the run
Is as good as despair for which to come

You cannot run away from your problems. They will follw you. That is despair for which to come.

Might as well be dead

If you're a victim of all these acts of despair, then you might as well be dead.