Look, the basic idea of building a champion the right way is matching the items with the skills. For example, annie takes AP because all her spells scale with AP, Pantheon takes AD because he has two skills that scale with AD.
Now, about cho'gath, he has four skills that scale with AP, and he has an ultimate which is great for a tank. However, he has no skills that increase/scale with AD, AS, or crit chance. The only sensible AD item for cho gath is atma's (and maybe frozen mallet, but i dont really know about that one), and thats because of his superhigh health.
So this crit-based build will never work, either take AP, or tank.