The trait reads as follows:
if the target is wearing nonmagical metal armor, its armor is partly corroded and takes a permanent and cumulative -1 penalty to the AC it offers. The armor is destroyed if the penalty reduces its AC to 10.
Sets of armor don’t have an AC bonus; the character has that. The gray ooze’s attacks reduce the armor’s AC bonus directly, so it doesn’t include any dexterity from the wearer.
This also prevents funny effects, like a set of armor being nearly destroyed on a character with dexterity, and then when he takes it off and gives it to a less dextrous character, suddenly falling apart.