They're leveraging Sunk Costs, a powerful psychological effect. Since you've filled out the standard parts of the form you're more inclined to click the Like button; bailing out late means abandoning all the work you've done. Even if the "cost" was something rather minor like this, you're likely to see less of a bounce rate than you would with a form that started with a "like to sign up!" intersital page before the form was filled out.
However, this is definitely a Dark Pattern as it's (ab)using psychological tricks to help the business encourage behavior that's good for them but not really good for the user at all, as Liking a page is now essentially signing up for marketing/shares from that page.
Also note you're excluding users without a Facebook account or who choose not to Like random companies/share your info with them...but that's likely irrelevant to the business decision at work here; those people wouldn't have Liked the company's page anyway. Since the focus is on that, not the user, user goals are abandoned; surely you see the problems this line of thinking can cause.
So, "should" it be done like this? It's a wicked thing to do and I wouldn't recommend it, but it may well increase conversion rates over a form where the "like" was required first. Of course I wouldn't recommend requiring the like at all; it's better to have one engaged user that actually reads your facebook posts and shares them than to have 50 users racing to unlike/hide your facebook posts immediately after signing up.