As of a few hours ago, thanks to a graciously merged pull request, you can export your own comments, in addition to your own posts.
To do it, you go to https://dev.to/settings/misc and select "Export content"
After a little while you'll get a nice email with an attached zip file of your content (in JSON).
An example of how comments look like:
If you want to know how it all started, check this other changelog post: