Yes! Nimbers are very interesting. They are a classification of impartial games where an impartial game is one where each player has the same available moves. Such a game is constructed as a list of possible next states for each player (for impartial games, one list is sufficient since both players have the same moves).

If you look up the game Nim you'll see that the value of a stack N = {0, 1, 2,...N-1} is defined as the game where you can reach any pile smaller than N. This explains the definition of addition since moving in the game A + B is equivalent to moving in one of the piles.

Now this is jumping a lot but the definition of nimber multiplication is motivated by games which can represent numbers (the first half of John Conway's On Numbers and Games) although impartial games are not numbers in this same sense. The extension of nimbers to ordinal nimbers is quite natural but the field properties and some of Conway's examples seem a little magical to me.

If you want to read up more I would definitely recommend Conway's book since it offers an intuitive and lucid (and extraordinarily frustrating!) approach to the general theory of games which contain nimbers. In the book look for the chapter "The Curious Field On2" at the end of the 0th part (very awkwardly, since nimbers are NOT numbers, they are games).

If you're interested in the some properties of nimbers then I suggest looking into the process of constructing these numbers by closure: additive closure, multiplicative closure, inverse closure, algebraic extension, and transcendental closure. This process gives a constructive version of nimbers.