HOW TO SAVE VIDEO MESSAGE – Skype Community.
Download and Run SQLite Database Browser [LMG or any capable of opening SQLite database]
Open the main.db file with it [LMG from the following location]
C:\Users\SYSTEM USER\AppData\Roaming\Skype\SKYPE USER\main.db
Click Browse Data >> Change the drop down option for the Table: to VideoMessages.
Under vod_path column, you will see the link. [LMG the link will be available on the video message that was opened on current computer]
Copy / Paste this link to your browsers address bar.