It's really up to the player to mold his/her race's characteristics. The rules don't state this explicitly, but I thought it was obvious that the type of race you play will have a great effect on the game. Let me explain.
In defense against your "magic > race particulars"-point I think you're separating "race" and "magic" too much. What kind of race you are will define what domain you choose, which in turn narrows the types of spells you can design. Naturally, it will also affect how the race fares in combat. An earthquake spell will not do any harm to a flying opponent, for example. If a burrowing race is fighting an aerial one, they must each design spells that are effective against the other.
As for numbers as a factor, I will require a relative score from all players. You're free to shape your race's strengths and weaknesses as you desire, which will then affect the reproduction rate to balance in terms of gameplay. If you want a race that's individually strong, they will simply not grow as fast. If you want a race that multiplies faster than any other, you'd best prepare for battle against other races.
Lastly, ripping off Tolkien (or defining the characteristics in prior at all) would ruin what I think is the essence of this NES. Which is to design your own race and have it play out against others in a magic world. That is also why I've left so much room for individual freedom. (Or is it this freedom that is irritating you?) Players are of course free to play your Tolkien Dwarves if they want to. It's just less original.
