Crowment works on any static site, GitHub Pages included: the comments load in the browser, so there is nothing to build or host.
Sign in to Crowment, create a comment widget for your site's domain and copy its app key from Install & Embed.
Save the embed code as _includes/crowment.html:
<script defer src="https://embeds.crowment.com/comments.js"></script>
<crow-comments app-key="YOUR_APP_KEY"></crow-comments>
Open _layouts/post.html and add the include after the content:
{{ content }} {% include crowment.html %}
If your theme comes from a gem (Minima, for example), _layouts/post.html is not in your site yet. Copy it from the theme first; bundle info --path minima shows where the theme lives.
Run bundle exec jekyll serve and open a post. Each post gets its own thread, identified by its URL path.
page-id: see Which thread a page shows.