How do Apple's USB Power Adapters allow for more power output than is possible in the USB 2.0 specification?

From my understanding, the USB 2.0 specification allows for a maximum power draw of 2.5w

No. Laptop USB 2.0 ports typically supply 5V at 500mA for 2.5W of power (Watts = Volts x Amps). However, this is not a hard and fast standard, laptops could, and often did, supply up to a full 1A of current for 5W of power.

but Apple's own USB Power Adapters allow for a maximum of 12w using a USB to Lightning cable. How is this possible...

It’s important to note that there’s no “Charging Specification” within the USB 2.0 Specifications. In fact, the word “charging” doesn’t even appear!

As for chargers (like wall or car), there were a number of tricks that manufacturers employed and Apple was no different. In fact Apple has a little bit if trickery to get more current into their devices and, in short, it involved not only using the +5V pin, but the data pins (D₊ and D_-) as well.

What Apple did was use some pull-up and pull-down resistors to get additional voltages of 2.8V and 2V on the unused data pins which resulted in an additional 1A of current!

^{Source: adafruit}

When creating the Minty-Boost charger, Lady Ada did an excellent writeup called The mysteries of Apple device charging. It’s an excellent read and the project is actually a fun intro into electronics. .

In the official website, it say "USB Power Adapter" without specifying which version of the USB port, why do you think it's 2.0 version ? 😉

Also, the power allowance from USB 2.0 specification is for powering connected devices (mice, keyboards...). For charging, there is Battery Charging Specification

You can read more in here: https://www.maximintegrated.com/en/design/technical-documents/tutorials/4/4803.html