Additionally, I have seen good AP Cho's and they can actually do really well (although I have never like them on my team and destroyed them easily against me). This guide tries to take the best of both worlds, but fails to achieve success in either way.
Sorry, just my experiences.

Many things wrong with this guide, and this is coming from a very experienced Cho' player. Cho'Gath is a tank, flat out. You are trying to build him as almost a caster hero, which he will always fail at compared to real mages. This build sacrifices the survivability of a tank for less damage than anyone and that just doesn't make sense to me. I can understand the build if you are going to play the whole game solo, but really you will never win without your team.
No matter how you build Cho', he will always end up with more than 3k health and not having Atma's Impaler is stupid. You will never be able to spam your abilities fast enough to overcome the damage increase and crit chance or the impaler.
Zhonya's Hourglass doesn't have CDR.
If you really want more AP, get your caster teammates to build Will of the Ancients.