Why is the Ancient Mariner only interested in telling his story to that guest only in The Rime of the Ancient Mariner?

Actually, the Ancient Mariner is driven to tell his story to almost anyone who will listen. He chose the wedding guest because, for whatever reason of his own, the wedding guest couldn't help but listen:

It is an ancient Mariner,

And he stoppeth one of three.

`By thy long beard and glittering eye,

Now wherefore stopp'st thou me ?

The Bridegroom's doors are opened wide,

And I am next of kin ;

The guests are met, the feast is set :

May'st hear the merry din.'

He holds him with his skinny hand,

`There was a ship,' quoth he.

`Hold off ! unhand me, grey-beard loon !'

Eftsoons his hand dropt he.

He holds him with his glittering eye--

The Wedding-Guest stood still,

And listens like a three years' child :

The Mariner hath his will.

The Wedding-Guest sat on a stone :

He cannot choose but hear ;

And thus spake on that ancient man,

The bright-eyed Mariner.

That's it: at this point the wedding guest is spell-bound and the Mariner begins his tale.

Maybe it should asked, Why, of all people, is a wedding guest, in general, chosen? Well, in some ways the tale that is told by the Mariner has the sense of a wedding about it. The Mariner becomes, after much travail, wedded to a new way of thinking about and loving life and the other creatures of the earth.

At first he felt a separation between himself and the albatross and all the "slimy things" that "did crawl with legs Upon the slimy sea." But at last he learned a deep truth:

He prayeth well, who loveth well
Both man and bird and beast.

He prayeth best, who loveth best
All things both great and small ;
For the dear God who loveth us,
He made and loveth all.

What a fitting little sermon for the Mariner and the wedding guest who both missed the more traditional wedding.