Because of the style isolation, which is a function of the Shadow DOM, you cannot define a global CSS rule to apply in the Shadow DOM scope.
This may be possible with CSS variables, but they must be explicitly implemented in the shaded component (which is not the case with this third-party library).
The workaround is to embed the style line directly into the shadow DOM.
var style = document.createElement( 'style' )
style.innerHTML = '.the-class-name { property-name: my-value; }'
host.shadowRoot.appendChild( style )
NB: this will only work if the Shadow DOM is modeset to 'open'.
2019 Chrome 73+ Opera 60+
CSSStyleSheet Shadow DOM :
var sheet = new CSSStyleSheet
sheet.replaceSync( '.color { color: pink }')
host.shadowRoot.adoptedStyleSheets = [ sheet ]