The majority of the routes are not bolted (see the breakdown of climb by type on this page): https://www.mountainproject.com/area/105833388/yosemite-vall...
They climbed The Nose, which seems to be a mix of trad (traditional, no fixed holds) and aid (placing temporary protection, then using gear to climb up to the protection, then placing protection, etc.) climbing - more on the different types of climbing here: http://www.alpineinstitute.com/articles/expert-tips/rock-cli....
More on The Nose route: https://www.mountainproject.com/route/105924807/the-nose
More detailed look: http://www.supertopo.com/topos/yosemite/thenose.pdf
You can see in the map of the route that some belay stations are bolted, and in fact the original ascent did use bolts - https://en.wikipedia.org/wiki/The_Nose_(El_Capitan).
> If it's dangerous it should be unlawful
The mountains, the oceans, and the deserts seem to be the last refuges of freedom. I hope that doesn't change.