Zombie Strike Ruling

I have an Un-rules question. I don't understand the UnFAQ's ruling on Extremely Slow Zombie and it gaining first and double strike. I don't understand why the Extremely Slow Zombie ends up dealing damage twice when it gains first strike and three times when gaining double strike. If I enchant a creature that deals damage in just the regular combat phase with a Cartouche of Solidarity, its damage changes from regular to first strike; it doesn't end up with double strike. Why is the ESZ different?

First strike and last strike are two different
abilities. Imagine for example that a creature has lifelink and squirrellink. If it deals combat damage, it doesn’t have to choose between gaining life or making squirrels. Here’s the quirky interaction. If you grant a creature with last strike, say Extremely Slow Zombie, first strike during combat but after first strike damage, it will deal damage during normal strike because that’s how first strike works. (Note that “normal strike” is not an actual term, I’m just using it for clarity.) Then because last strike has the same interaction with normal strike as first strike does, last strike damage wouldn’t happen because damage happened during normal strike. This is due to the fact that each first strike and last strike have a relationship with normal strike. They don’t though have a relationship with each other.

Cartouche of Solidarity Creatures Deal Damage Double Strike Enchant Extremely Slow Zombie First Strike Lifegain Lifelink Rules Squirrel Un-sets Zombie