The 1.0 equivalent of core-media-query is iron-media-query, which is here:
The demo for this element could be better. The iron-media-query element's queryMatches property can be data bound to any other property you like, and you can use data binding to set attributes on other elements, to enable styling. You can also set an observer on that property and run arbitrary code when it changes.
Here's a jsbin that shows setting an attribute on a local DOM child, setting a class list on a local DOM child, and toggling a class on the host element, all based on a single media query:
The class list one uses the iron-flex-layout classes to change layout. (You probably won't use all of these approaches in the same element -- this is just to demonstrate some of the possibilities.)