He has to hold office in the line-of-succession to be eligible. He does not hold such office, therefore he is ineligible.
It is simple, and it it is meant to be simple. But lawyerese always leaves an opportunity for "nuance" (feh) when the lawyers don't intend to.
Why, oh WHY, couldn't have said: "If you have been President twice, then you can't be President again or Vice President."
I encourage you to read Eugene Volokh's thoughts on the subject, to which I provided the link above.
As to your question regarding why the language isn't different, you'll have to ask the drafters of the Amendment (if any are still alive).