Does an official I2S specification exist?
in short, no.
the I2S specification originally put forward by Phillips is seemingly not maintained (or available through official channels), and the vast majority of interfaces which are referred to by this term do not follow the original Phillips document. 

in general, there is no need for an official specification. the I2S bus is designed for board scale use (between chips on the same PCB as the name implies). this means that as a board designer, both ends of the bus are connected to known and fixed ICs, and the bus specification is defined by the datasheets of the master and slave devices you are using. both codecs and host processors generally specify their requirements very well, and the designer must compare the 2 devices to check compatibility with each other rather than to some 3rd party specification.

you didn't explain why you want one, but I can imagine 2 situations where you might want an official specification to follow rather than going by the ICs datasheet. if you have another, let me know and I'll update this answer

you are designing an IC which will feature this interface:
in which case your goal is to allow board designers to use your IC to connect to other ICs. since many devices don't follow the Phillips spec anyway, your best bet is to look at what is being used in the field. many devices allow the clock and frame sync (word clock) polarities to be configured, and the data MSB position relative to the frame sync signal to be adjusted. The original spec had the MSB delayed by one bit clock to allow a simple receiver to be made using 74 series logic - rather pointless today when codecs are cheap and readily available, but the format is still supported by many interfaces. TI have expanded the interface to allow multi channel audio etc.

choose an implementation which is very flexible, or which is compatible with most other implementations depending on what you want your chip to do.

you are designing a product which will connect to other products using I2S:
in this case, you are not using I2S in its intended manner. I2S is not meant for cabling, and doesn't feature any kind of command channel that could identify device capabilities (eg, bit clock frequencies, word length). in this case you should look at other protocols which are intended for this use and will be better specified. I would be surprised to find many (any?) products which feature an I2S port on the market. instead, look at S/PDIF for example: https://en.wikipedia.org/wiki/S/PDIF