Let's look at the alternatives:
The Islamic Calendar - has before and after the "Revelation to Mohammed by Allah of the first part of the Quran;" I believe that one puts us in 1300-something.
The Judaic Calendar - starts at the arbitrary year of the "Seven Days of Creation," with no acknowledgement of time previously; I believe that puts us at 5400-something.
The Thai Royal Calendar - I can't remember it's inaugural event; I believe it's currently at 2200-something.
The Old Chinese Calendar - Not only goes back to sometime in the 4th or 5th Millennium BC (or BCE), but groups years into units of twelve (the Chinese "Zodiac" years), not a simple progression.
The Maya Long-Count Calendar - a very accurate and precise count of over 4000 years of time (inaugural event not clearly known), but it ended it's official count five years ago.
The Punjabi, Persian, and Classical Greek and Roman Calendars also come to mind, and I'm sure there are many others I'm less familiar with.
However, in all of these cases, it's not nearly as simple as just renaming BC(BCE) and AD(CE). Many of these calendars are still officially lunar, not solar, to boot.
You left out the Imperial Japanese calendar, which dates everything from a 'start date' of the Sun God/First Emperor, so we are now in Year 4076. I believe.
Romans frequently dated things from the 'founding date' of Rome itself, many of the Greek writers dated from founding of the individual city states or from the first of the Olympic Games.
Greeks and Romans for two, used 'years' that started with the Summer Solstice, so their years actually overlap the 'Christian' dates by half.
Many, many civilizations seem to have 'dated' everything based on the ruler (or Republican Roman Consul): "X year of the reign of Z" - which is pretty arbitrary no matter how you look at it.
BUT having the game use a specific Christian dating designator for a multi-cultural game is pretty lame, even if the dating system is used almost universally in the modern world. A far better and more 'Immersive' system would be to have each Civilization start with a date based on the founding o the first city/first ruler, and later change that to the founding of the first religion/Great Prophet or some other Arbitrary date based on the development of the Civ: Discovery of Astrology, for example, might allow you to change to a Mayan or Babylonian-type calendar, a Golden Age might allow you to start all new dates from the start of the Golden Age, etc.
Oh, and as others have pointed out, the 'end of days' in 2012 was only the end of the Long Count Cycle. By design, there is no End to the Mayan calendar, it's continuously cyclic. When US archeologists asked natives of the Yucatan (Mayan) area about it, they simply said 2012 meant "It's time to get a new calendar!"