The rules for polymorph state that you lose all abilities that depend on your original form.
While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form (such as keen senses, scent, and darkvision), as well as any natural attacks and movement types possessed by your original form. You also lose any class features that depend upon form, but those that allow you to add features (such as sorcerers that can grow claws) still function. While most of these should be obvious, the GM is the final arbiter of what abilities depend on form and are lost when a new form is assumed. Your new form might restore a number of these abilities if they are possessed by the new form.
Does this mean that a vampire loses all his vampire based abilities when he uses the vampire ability change into a wolf? If so does that mean the vampire is now a living creature with a CON score and no vampire weaknesses? Technically that would mean he loses the ability to change shape so he cannot actually use this ability. What abilities does a vampire or other template creature lose when he uses a polymorph effect? Or do you change into a template creature of the type you assume?
The rules for polymorph state that you lose all abilities that depend on your original form.
While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form (such as keen senses, scent, and darkvision), as well as any natural attacks and movement types possessed by your original form. You also lose any class features that depend upon form, but those that allow you to add features (such as sorcerers that can grow claws) still function. While most of these should be obvious, the GM is the final arbiter of what abilities depend on form and are lost when a new form is assumed. Your new form might restore a number of these abilities if they are possessed by the new form.
Does this mean that a vampire loses all his vampire based abilities when he uses the vampire ability change into a wolf? If so does that mean the vampire is now a living creature with a CON score and no vampire weaknesses? Technically that would mean he loses the ability to change shape so he cannot actually use this ability. What abilities does a vampire or other template creature lose when he uses a polymorph effect? Or do you change into a template creature of the type you assume?
The answer is right in what you linked: The GM is the final arbiter of what abilities depending on form are lost or kept. That being said, it's essentially a "Expect Table Variation" answer, and although it's not a good one, it's the best RAW answer provided.
That being said, the RAI I gathered from spells like Beast Shape (which is what the Vampire's Wolf Form emulates) tells me that they only assume the form of the creature, it doesn't change their type or subtypes, meaning spells affects them as if they weren't polymorphed, which leaves the factor that they're still undead or a vampire while having the form of a wolf.
As Darksol says, the vampire keeps the Undead type, and it still doesn't have a Con score either. Ability scores only change when polymorph effect specifically say they in do, this case, Change Shape, not at all.
As far as what various abilities the vampire will lose shape changing away from a vampire, I would recommend looking at the Undead Anatomy series of spells. These spells tell us what abilities are gained by changing form into that of an undead. It is logical that similar abilities would be lost when one polymorphs away from the undead form into the form of a living creature. Of course as Darksol points out, per rules the GM is the final arbiter of this, even without house rules.