I'm looking for a good solution to this issue.

Basically the house is a 1970s era PJ area house that came with the above mentioned flooring in the living room area. It used to have a slight shine to it that I remembered as a little boy living in the house but now its mostly "matte" and full of scratches either from furniture dragging or the years of riding tricycles indoors.

It's now having that issue that you could sweep the floor and while mopping it you will have blackish stains as if some cement or fine sand is being released. If you walk on it with some white socks then its a sure thing that you'll be having grey socks in no time.

Are there any solutions to this that's either permanent or semi permanent?

Been told it isn't similar to broken marble that you could grind and reseal it numerous times. However have also been told to try grinding it and having it sealed again. Kind of not really an option as the house has over 40 years of junk and the living room has some built in cabinets that are difficult to remove.

Does anyone know of any other solutions to this?

Polish the floor.

Normal job. But you need to move your furniture

Either removed all built-in to polish and wax or just do the uncovered area.