In-game, Inca military units reuse the Incan Huaminca's dialogue in Age of Empires III, while their Villagers, Kings, and Monks have new dialogues, all are in Quechua, also known as Runa Simi.

Villagers
Ari - Yes
Rimay - Hey
Ñam - Ready
Kamachiway - Command
Unanchasqa - I understand
Ripuchkani - I'm going
Kunanqa - Immediately
Aymuray - Gatherer
Willuy - Lumberjack
Kasachiy - Hunter
Challway - Fisher
Tarpuy - Farmer
Qurita hurquy - Miner (f)
Allamuy - Miner (m)
Sayarichiy - Builder
Allichay - Repairer

Military
Ari - Yes!
Jai - What?
Chjaaku
Gorriya
Mut'uy - Fell
Aytippe - Attack!
Qu'utiya - Attack

Monks
Ari - Yes
Kamachiway - Command
Qamta yanapanaypak - At your service
Wiraquchanpa raymin - In the name of god
Richkani - Right
Hap'inim - Understood
Utqaylla - Immediately

King
Kaypim - Here you go
Imaraykum qhamzapakuy - What do you want
Willamuspa - Reporting
Mañasqaykitam rurasak - I will do as you ask
Kusikuyniypak - By my grace
Munakusqaykikamam - As you requested
Kayhina rurasak - I shall do