It's not a "transformer" it's a DC-DC step up regulator that uses the LTC1871 chip. This is way more efficient than a transformer.
If the coil's max output was 25W at 4.17A - 6V for example and you had a converter to step the voltage up to 12v with 100% efficiency it would be 25W at 2.1A - 12V.
The wattage stays the same but the amperage is less at 12V.
The efficiency should be around 90% when converting 6V to 12V with that board so 25W at 4.17A - 6V would convert to 22.5W at 1.88A - 12V
Now the coil will only output around 6V max even if the engine is at a high RPM if the load is more than 25W because stock it runs 26W of lights at 6VAC also the AC buzzer horn takes 9W so the max load stock is 35W, but if the load is less than 25W and the voltage can get out of control without a step down regulator.
The LED lights that replaced the bulbs are brighter and use way less power, the regulators keep them at max brightness at any RPM, but because they use way less there is a lot more current left to run other things like the camera in the video.