No. The Imprisoning War was about stopping people from entering the Sacred Realm, and halting Ganon's forces that were leaking out. This part of the backstory was referring to the Sages(probably the Ancient Sages) hiding the Triforce. This part of the bs was probably referring to the Era of Chaos.
Ganon's backstory is retold partly, mainly the part about him being the human thief Ganondorf who entered the Sacred Realm, claimed the Triforce, and became the Demon King, but then it skips over ALttP and the Game Boy (Colour) titles(like how SS, TMC, and FS were skipped over) nad talks about a different event that has some huge differences from ALttP;
ALttP:
-Seven maidens, not sages; Zelda is one of the maidens
-Ganon is killed
-The Triforce is united
ALBW:
-Seven sages, not maidens; Zelda is not one of the sages
-Ganon is sealed with the ToP, not killed
-The Triforce is divided
This event is noticeably different from the events of ALttP, and happened prior to ALBW, just like how the backstory for FSGBA is a seperate event involving than TMC, despite FS being after TMC.