I know that bonuses of the same type other than dodge do not stack. However, the natural armor increase in this template is not labeled as a bonus. Does that mean it would stack with something like the spell Transformation and/or an amulet of natural armor? Or is it just that it's simply poorly worded?
Go ahead and add the devilbound template's AC increase to the creature's natural armor bonus (even if one isn't listed)...
(I'm hesitant to use the word stack as that's usually reserved for bonuses, but, casually, yes, it stacks.)
The template devilbound has the following entry:
Armor Class: Natural armor improves by +4.
This isn't a bonus but an improvement. Unlike, for example, the spell barkskin, which grants an enhancement bonus to a creature's natural armor, this modification increases the creature's existing natural armor bonus and isn't a bonus at all. This means, for example, a typical devilbound troglodyte Ftr5's natural armor bonus is +10, and a typical devilbound human Ftr5's natural armor bonus is +4.
Because it's an improvement rather than a bonus, it's compatible with the amulet of natural armor (which grants an enhancement bonus to a creature's natural armor), but only compatible with the spell transformation if that spell's in effect when the creature gains the template, as explained below.
But if the creature's already devilbound, don't add the AC bonus from the spell transformation
That is, the natural armor bonus granted by the spell transformation will overlap with, not add to, the natural armor bonus of a creature already possessing a natural armor bonus.
This makes for the weird situation wherein if a creature casts the spell transformation (which grants a natural armor bonus) then, while under the effect of the spell (which only lasts 1 round/level), subsequently gains the template devilbound ("Quick! Where do I sign?"), the template devilbound's improvement to natural armor improves the natural armor granted by the spell... then goes back to the new normal +4 from the template when the spell's duration expires, and, in all likelihood, the caster won't be able to get his AC that high that way again.