Looking at my datasheet it says, "provides 131,072/262,144 bits ... organized as 16,384/32,768 words of 8 bits each", and "128K (16,384 x 8), 256K (32,768 x 8)"
www.atmel.com/atmel/acrobat/doc0670.pdf
Hardware manufacturers of memory products tend to describe their products in terms of capacity measured by the number of bits available. This appears to be their convention and is fairly standardised. The number at the end of the device name usually reflects this, eg AT24C128 = 128K, that is 128K bits.
At least the using of a standardised unit of capacity (bits) makes it easy to compare capacities of various components without the confusion of which is larger; 128Kb or 64KB, having to read further to determine if "Kb" or "KB" is used to mean bits or bytes.
An AT24C128 has 131,072 bits (128Kb), 16,384 x 8 (16KB)
An AT24C256 has 262,144 bits (256Kb), 32,768 x 8 (32KB)
As to the use of "word"; this was originally a generic term for a unit of memory of some bit-width and is still used that way in many cases. It is not necessarily 16-bits ( 2 bytes ) or 32-bit ( 4 bytes ).
While "byte" is more universally taken to be 8-bits, by not using the term in the datasheet it avoids confusion and complaint where a byte is not considered to be 8-bits. It is however fairly easy to convert between the units manufacturers use and what programmers usually use -
Number of bytes = Number of bits / 8
Number of K bytes (KB) = Number of bytes / 1024
Number of K bytes (KB) = Number of bits / 8192
Also note that "K" when used by programmers and hardware manufacturers is usually taken to be 1024 ( 2 to the power 10 ) , in some cases, particularly for disk and removable storage ( SD Card etc ), it can mean a decimal 1,000.