Go to 4:11, you can see that the skills are....
Magic: alchemy, illusion, conjuration, destruction, restoration, alteration, enchanting.
Combat: smithing, heavy armor, block, two-handed, one-handed, archery, light armor.
It's seven skills in each, not six. We just can't see the stealth skills. Apparently both archery and light armor are now in the combat category, and alchemy is still in the magic tree.
No, 6 skills each and Alchemy and light armour are in Stealth