For those of you who are Admirals Club® members, I have verified some details with Admirals Club® (they returned my e-mail with a telephone call today), as follows (and paraphrased, not verbatim):
1) The Admirals Club® logo on the back of the card is your proof of membership; you have all the normal AC member privileges. (As
TheDudeAbides says below, the card is linked to your AAdvantage number - a quick lookup of that will show your status.)
2) The Club membership validity is the same as the card validity (shown on the front).
3) Access as permitted at clubs with reciprocity agreements, such as the JL Sakura Lounge at Frankfurt, AS Board Rooms in Seattle, Portland and Anchorage, AY Finnair Lounge in Helsinki, MA Malév and Millennium Lounges in Budapest, IT Kingfisher Lounge in Delhi, KA Dragonair / Cathay Lounges at Beijing and Shanghai - as long as you are flying on AA the same day. See
here for details. Also admission to International Qantas Clubs - "30 international lounges operated by oneworld partner, Qantas (must be traveling on Qantas operated flight for access to Qantas lounges); see
here for details.
I have been assured all corresponding / reciprocal lounges have been given the information - there should be an illustrated guide that includes the Citi ExecutiveSM / AAdvantage® World EliteTM MasterCard® so you show it and required documents; if you have trouble and meet all the requirements listed here and in the referred pages, ask to speak with a supervisor.
And
Pucnit below also says they will reissue cards - perhaps the Club logo will be more visible.