After some searching I have come to the conclusion that it is not possible to retrieve CSS styles using the PHP DOM parser. Can anyone confirm that?
An element can e.g. be identifyed by its ID. If that element then has a style attribute (an element style style="abc"), this attribute's value can be retrieved too. But if the element's style is defined by an id from a CSS selector, PHP seems not to have any direct access to the styles.
The only workaround I see is parsing all linked CSS files and checking if there are any styles assigned to that ID. Is that right?