The Mariner is compelled to stop someone every so often to tell that person his story.  This comes from Part I of the poem.  The "glittering eye" that the wedding guest notes is the eye that suddenly recognizes the individual who must hear this story.  The bright eye is mentioned again at the conclusion of the poem as the Mariner goes on his way again in Part VII.

The dice game being played by Death and Life-in-Death is described in Part III.  That Life-in-Death wins is bad news for the Mariner because it means that he must suffer.  His crew mates all die and he is left alive to atone for his sin of killing the albatross.  He must live to see each of those men die and as each dies, he looks at the Mariner and curses him with his eye making the Mariner responsible for each one's death.

"By thy long grey beard and glittering eye" is said to the Ancient Mariner by one of the three gallants who were going to a wedding feast.  The Ancient Mariner then proceeds to tell the wedding guest his tale.

"The game is done! I've won! I've won!" is said by Life-in-Death, who has been in a dice game with Death for the Ancient Mariner.