Ok so before i did the Shaman, but now i want to get into 2 "Extinct" races that i feel can be mostly replicated in-game. Remember that this is mostly only going to appeal to heavy RPers. 1st is the Ayleid or Heartland High Elves of Cyrodill.

Ayleid
Race: Altmer
Skill Trees: 1H/2H/Block, Destruction, Alteration, Light Armor, Enchanting, Smithing
RP Items: Elven Armor/Weaponry
Stone: Lady, Mage, Apprentice, Lord
Shout: Any
Discussion: The Ayleids are pretty much High Elves so you can very much play accordingly. Think of the Thalmor soldiers in Elven armor you encounter in skyrim. It is like a Light Armor Battlemage of sorts. What really makes this class stand out is the RP possibilities, otherwise it is just an Elf. The Prime Weapon is up to you whether it be 1 Handed with dual wielding or shield or 2 Handed for pure offense. The Destruction magic should provide an advantage over specific enemies who are weak to elements while Alteration serves to make you stronger with spells like Oakflesh. Smithing is for making your own Elven armor and keeping it upgraded with Enchanting added onto that. Now if anyone thinks that the class is nothing special r is restricting then any Elfy build who just wears Elf armr can be considered Ayleid but this is my personal take on it.

Next is the Dwemer or Deep Elf/Dwarf. We are starting to learn a lot more about them now and can better replicate their long lost race.

Dwemer
Race: Bosmer (Altmer are too tall and magic-oriented but Dunmer MAY suffice)
Skill Trees: Smithing, Heavy Armor, Block, 1H, Enchanting
RP Items: Dwarven Armor/Weaponry, Transmute Spell, Complete the quest "Unfathomable Depths"
Stone: Atronach, Lord, Steed, Warrior
Shout: Any
Discussion: All of these stats are rather obvious but when you upgrade them correctly you will be making Dwarven Centurions cry. Dwarven Smithing is the most profitable Smithing available. Take a follower, head to Black Reach and gather as many Dwarven junk parts as you can, melt them down into dwemer ingots, make great equipment, profit. Also completing Unfathomable Depths will make your use of Dwarven gear more effective as well as smithing.

Now i must stress again that if you care not for RP then these classes are not for you but i have played both and they are both great. I have used them both (same names and preferences) in Skyrim and Oblivion. Comments welcomed

No race really fits, besides the Dwemer were quite magic oriented if I remember correctly.
Therefore I would add magic skills to it, what you have is a warrior.
RP items, seems ok, I would add some books and maybe staffs, dwemer artifacts to decorate whatever place you choose to settle down in.
Stone: seems ok, but as I said your build is heavily combat oriented so I would probably also add Mage and Apprentice as well.
Shouts: well this is really more of a Dovahkiin aspect so I agree with any.

A nice build though, it just doesn't scream Dwemer to me.
The Ayleid build looks nice, I would add the atronach stone to the list. Also I don't know if I would spec any light armor.

If i had to put magic onto the Dwemer's list i would go with Alteration and MAYBE throw in alchemy but then again it is anyone's preference

This is why I make class build instead of race builds, it's more defined, and besides we don't know that much about any of the races to make any good RP builds, epecially since I guess like every other race the Ayleid and the Dwemer were different from one another, not every dwemer was the same.
But as I said those bulds are pretty nice, the dwemer one just doesn't fit with my interpretation of the dwemer thats all.

Well those are really my only race builds, my others are classes. I make lots of different things to test. My other builds are Bounty Hunter, Pirate, Bard, Paladin...oh and a Dremora but that IS a race build

I think that for both races Altmer would fit best.
Altmer are the closest to Aldmer, of who all elven races descend. The Dwemer probably were not that physiologically different from original Aldmer, or Altmer, their differences were more of a philosophical and religious nature.
Races like Bosmer, Dunmer and Orsimer have had their appearance, and probably nature, extensively changed by divine intervention.

Given the notion of Dwemer as scientists/ technomancers maybe a Skyrim Dwemer would be interested in collecting legendary artifacts, such as the Daedric ones? Just a roleplay idea. Enchanting would fit as a skill.

Mind that we do not know that much of both races, and probably more of the Dwemer than the Ayleid.
Ayleid were interested in magic, specifically starlight.