https://www.overclock3d.net/news/software/age_of_empires_iii_definitive_edition_is_now_available_to_play_for_free_on_steam/1
 
The whole game isn't available for free, but free users will get access to a lot of content
 
C gamers can now play Age of Empires III Definitive Edition for free on Steam
Xbox Games Studios have given PC gamers a new way to play Age of Empires III; Definitive Edition, a free trial version that will feature a rotating set of civilizations, access to skirmish and multiplayer battles, and access to act 1 of the game's Blood, Ice, and Steel campaign. To access the full game, PC gamers will still need to purchase the base edition of Age of Empires III: Definitive Edition, with free trial users acting as a way for new players to try out the game without any financial investment. The free trial also has no time limit, allowing gamers to enjoy new free content as the game's weekly roster of free civilizations rotates between nations. Free trial players will also be able to participate in global events and unlock cosmetic items for their heroes.
 
Age of Empires III: Definitive Edition's free trial is now available to play for free on Steam. All gamers need to do is download the game on Steam and play. To access all of Age of Empires 3's content, PC gamers will need to purchase the "Base Game" edition of the game on Steam. Currently, this base edition of Age of Empires III: Definitive Edition is currently available for £14.99.
 
If you like the game the purchase price is very reasonable in my personal opinion.