Why does a single AND gate need 60 transistors?
There can be several reasons why more than the minimum 6 MOSFETs (4 for an NAND + 2 for an inverter) are used in this IC:


As stated in the datasheet: 



  The internal circuit is composed of multiple stages, including a
  buffer output which provides high noise immunity and stable output.



The output will be made using fairly large (not minimum size) transistors. There are always "folded" meaning multiple transistors are combined into one large one where drain and source diffusion areas are shared between two transistors. This behaves as one large transistor but could be counted as many if you want a higher transistor count.
The ESD protection at inputs and outputs of IC fabricated in modern CMOS processes often uses "grounded-gate MOSFETs" instead of the more traditional diodes.
An "ESD clamp" circuit is needed between the supply pins, such a circuit consists of a couple of transistors.
Digital circuits (like this AND gate) often need on-chip supply decoupling. These are called "decap cells". These are capacitors between the supply rails. These capacitors are mostly made by using the Gate-Drain/Source capacitance of Transistors.
In CMOS processes the MOSFETs are the most "basic" components, they are also the most controlled component and most flexible ones so IC designers prefer to use a MOSFET whenever possible.


All-in-all it is "quite easy" to need 62 transistors to make a seemingly simple function like an AND gate. That's also because this IC is "a bit more" than just a simple AND gate. The AND gates in more complex circuits like CPUs, microcontrollers etc. will often only use 6 transistors. But these aren't "stand alone" AND gates like this IC.