The Free Streaming part is just a trick don't fall for it.
They do this so you will remember just how good the show is, then the next week they wont offer it, but they will for sure send you an email stating that DireCTV still has it. They may even offer you an extra $20 to switch to someone else.
They will also take the data on how many DISH Customers watched it so they can use the info in negotiations for a better settlement with Dish.
One could also look at it the other way, if every dish customer signed up and watched it, AMC would take the data to show Dish, see, you really must settle and add back AMC as they really do watch it- they could switch to someone else if you dont.