What is the meaning of "b'Chumam Ashis Es Mishteihem"?
Rashi: I will arrange that their drinking parties are at the time of heat, so they will become drunk.
Radak: (The night that Bavel was captured, Belshatzar made a great party (Daniel 5:1). A hand wrote on the wall of the palace.) At the time of their heat, at the party, I will make their parties evil. It will be reversed to mourning and great fear - "Belshatzar was very afraid and his appearance changed and his nobles panicked" (ibid., 9).
Why does it say "Lema'an Ya'alozu v'Yashnu Shenas Olam"?
Rashi: Amidst intoxication, they were destroyed and killed, and the city was conquered - "Belshatzar said due to the wine (inebriety)...; they drank wine...; that night king Belshatzar was killed...; and Daryavesh ha'Midi received his kingship" (Daniel 5:2, 4, 30, 6:1).
Radak: I will inebriate them at the party so they will sleep forever. Others who are drunk sleep amidst inebriety, and afterwards waken. These will rejoice amidst drinking from the Kelim of the Mikdash, sleep forever and not waken - "Belshatzar was killed" (Daniel 5:30).
Radak citing R. Yonah: They will go crazy and shake. In Arabic, Alaz is muteness and trembling that seizes some ill people before death. It looks like they are laughing. And so he explained "Ra'asechi Az Ta'alozi" (11:15).
Radak citing Targum Yonasan: So they will not be strong, and they will die a second death, and not come to the world to come ("v'Lo Yakitzu").