The DMCA.com badge works by signalling the existence of websites and pages to a server which then indexes each page of your site marked with a DMCA.com badge. Classically, most websites are separated by distinct addresses where pages and their content are returned directly by a server with little or no processing needed in between.
Single-Page-Application websites differ in that they leverage the end user's browser to do the work of routing the requested page and loading its content. This can be a problem for web bots that do not perform this rendering process themselves, as they will only see the application itself and not the requested content.
Currently, the only option for crawling a SPA site is using a third-party page rendering service. These services are typically used to return the rendered versions of a SPA site page for web crawlers like Google or Bing that also do not render SPA pages.
You can use these rendering services with the DMCA.com web crawler similarly to these search engines by enabling use with the following user-agent string: "DMCA.com Page Protection Crawling Service"
If you enable your site to return raw HTML content using one of these services to the user-agent specified above, DMCA.com will index your content as usual.