Thanks for the bug report. I’ve fixed everything and added an exclusion list.
Thanks for your interest!
The plugin will technically work on a multisite installation, but it was not specifically designed for it. Each blog has its own settings and broken-links list, and there is no Network Admin dashboard to manage all sites from one place. WP-CLI support is also not available yet. This is version 1.0.0, both centralized multisite management and WP-CLI commands are planned for the next release.
Best, Archivarix Support