No, they are two different companies.
Think about this question. Will Dunkin Donuts accept Starbucks gift cards? Will Target accept Macy's gift cards?
As far as i can tell, the 2 theater are not related. According to AMC site, cards are "Usable up to balance only to buy goods or services at any AMC Theatres®, AMCLoews®, AMC Showplace, Cineplex® Odeon, Magic Johnson and Star theatres in the U.S. Not usable to purchase gift cards. Not redeemable for cash unless required by law. Not a credit or debit card."
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