I'm trying to find the actual name, if indeed there is a name, for the variant played at "itsyourturn" that is referred to there as "Backgammon Race". It is similar to the well-known "Acey-Deucy" except that you don't roll again if you roll doubles and there is nothing special about rolling a 1,2. I did a search and the closest i could come up with in terms of an established name is: "Dutch Backgammon", with the difference being that there is no restriction on movement of checkers in "backgammon race", ie, you can move the checkers that have been brought on as you choose without having to have bring them all on, and also in "Backammon Race" cube play is involved which I don't think is the case in Dutch Backgammon proper.

Also, are there any books or strategy material for this form of the game?

A couple of possibilities. It could be a game called "Moultezim", which is popular in the Middle East, or it could be a variation of "Tric-Trac", which was the dominant form of the game in Europe in the 17th and 18th centuries.

A good resource for backgammon variants is a book called "The Seven Popular Games of Backgammon" by Frantzis. It's out of print but you can probably still find it on used book sites.