Upvote:4
Unfortunately the link to the video has died due to link rot. However, I assume you mean the dots to the right of this list of trains departing (for example) from Roma Termini:
File:Tabellone delle partenze Roma Tiburtina 01.JPGCC Attribution 3.0
Blinking dots indicate that the train is departing (in partenza, in Italian). This is replicated in the digital version of the departing train dashboard, which can be found at this link:
I cannot say whether this means that the train is closing its doors, is about to depart, or has departed from the platform.