The next sentence: "The lounge is only available to transatlantic passengers holding business class tickets and airline club cards. For queries regarding lounge access please contact your airline directly." So I certainly wouldn't take the airport's blurb about lounge access as indicating that AC members get access.

AA lists this lounge on their web site, saying "Must present a boarding pass for same day departing travel on an AA marketed and operated flight (flight sold with AA flight number and flown on AA aircraft)." No mention of Admiral's Club membership card required (as most partner lounges that accept members say), so it's not clear to me what the rules are. It's not even clear whether Sapphire/Emerald in coach will get access; since it's a third party lounge, the oneworld rules don't require status-based access.