Her videos show her engaged with various hardware projects-- making them and explaining them.

The article concerns the slander that these projects aren't hers; that she is merely a mascot presenting the work of her (male, engineer) boyfriend.

To notice "a mind at work" in the videos, is to suggest that the videos are her authentic work.

In general, a mind at work is analyzing problems, being creative, combining old ideas into new ideas, planning for the future and in general actively engaging the world. This is contrasted against more passive thinking. For example, complaining about something instead of actually doing something about it.