From a purely physical point of view, being "under pressure" means having a force applied to you. Our atmosphere is constantly applying a force on us from all sides, so objectively speaking we are constantly held under pressure. Our bodies cannot function without that pressure, like in the vacuum of space.
The linked website doesn't explicitly state so, but I assumed the liquid gold would enter the mold without pressure. I've been proven wrong, please check the answer of OP.
My original assumption was that in order to "insert the metal under vacuum into the flask" the molten metal must be in a vacuum as well. It is poured into the mold and flows down by gravity alone. Depending on when the vacuum is released (while the metal is still liquid enough to flow or not), the atmospheric pressure will push the gold into the smallest nooks and crannies of the mold without leaving air bubbles behind.
The opposite of that process would be centrifugal casting, where the mold is spun in a circle and the centrifugal force pushes the material into the mold. You can read more about both casting methods here (Thanks to Allison C. for the hint). I see no indication that this process is used by this specific manufacturer. If you ave questions or concerns about their process, maybe ask them directly for more detailed information.