victory song
凱 centers on a triumphant song or celebration of victory. The meaning is specific to the joyful music or shout that marks a win.
凱 combines 豈 (a phonetic element associated with joy or triumph) with 几 (a table or stand), together suggesting a celebratory display or song of victory. The exact historical development is uncertain.
The left side 豈 looks like a drum on a stand (豆 over 口) with a mountain-like top, and the right side 几 is a table. Imagine a victory drum placed on a table, and a song of triumph rings out.
For ガイ, picture a victorious guy singing a victory song: guy -> ガイ, and his song celebrates the win.