Bugle, i am a woodturner primarily and i have heard of and do use a wax/mineral oil finish on some of my pieces. Many antique furniture owners, furniture restorers, or heck new furniture builders such as yourself for that matter, have used paste wax similar to what you are making reference to for eons on everything ranging from the old fashioned two handed rough-cut tree saws for lubrication to threads on wood screws prior to insert and even their dried skin on their woodworking hands.
There are different compositions however that contain drying agents that create some form of drying. This stuff never really dries completely...its a wax and some of the commercial compositions include a beeswax and carnauba wax consolidated with tolulene, Briwax brand to be specific.
This facet of not drying out thoroughly has its advantages. Pieces finished in this capacity are typically conversation pieces anyway and this provides great protection from human oils as individuals desire to touch and handle the piece. This 'turning' paste is really good at retarding human oils and can be quickly buffed back to a sheen after handling with a fine knit cotton cloth.
Not quite sure if the video you are making reference to actually referred to a paste wax and mineral oil or was the wax? - bee's wax - do you recall?
I am a beekeeper and i make my finishing paste out of pharmaceutical grade mineral oil and bees wax collected out of my hives. The bees wax has to be melted in a 'working pot', never use a good pot and the mineral oil stirred in either in equal proportions to the melted wax or a little less. Remove from heat and pour into used, empty shoe polish containers, allow to cool and harden. The little tin shoe polish containers make excellent go-to containers as you are turning on a lathe.
It is possible that you could have seen a finishing wax that was created by using the woodworker's paste Briwax and mineral oil to cut it down a little for better finishes on the lathe.
But yes, this stuff can be used on new woodworking projects just understand that it will not cure, but oft times that is not an issue, for on many drier woods like Walnut it can be worked deep within the pores of the wood with a quick, hand wiped friction application thereby leaving you with a deeply finished piece.
The decision to use it or not use it is all personal preference i suppose just as some prefer Hanes over Fruit of the Loom...at any rate i would suggest playing around with some of this stuff, it has other beneficial realms other than just the finishing of wood as i have mentioned earlier. You can use the Briwax composition on your lathe bed, table saw table to create a highly friction free surface or either use it on your blades or other metals to prevent rust.
The mineral oil/beeswax composition can be used in many varying capacities as well.
Take care, Chris