“For just as you drank on my holy mountain.” Although it is not mentioned in Scripture, this no doubt refers to the Edomites drinking themselves drunk in Jerusalem, celebrating the Babylonian (and their own) victory over the Judeans.
“the nations drink continually.” The “cup” and drinking are often used in Hebrew literature to refer to God’s judgment and wrath. The figurative language is not expressed in the complete thought that prose is, but the idea is that Edom drank in victory, but now Edom and the nations will drink the cup of God’s wrath. They will “drink continually,” and “drink and swallow down” meaning that there will be wave after wave of God’s wrath until there is nothing left of those nations. This verse is not about personal judgment, it is about the judgment of the ungodly nations, and that they will disappear from history.