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Interestingly, The Last Samurai was extremely popular in Japan. It sold more tickets in Japan than the US (even though the US population was over 2x as large in 2003). This is in stark contrast with basically every other Western movie representation of Japan (edit: I think Letters from Iwo Jima was also well received and for somewhat similar reasons).

From what I understand, they of course knew that it was alternative history (aka a completely fictional universe), but they strongly related to the larger themes of national pride, duty, and honor.

Tom Cruise portrays Nathan Algren, an American captain of the 7th Cavalry Regiment, whose personal and emotional conflicts bring him into contact with samurai warriors in the wake of the Meiji Restoration in 19th century Japan.

And yet, it is Cruise's face rather than Ken Watanabe's on the poster.

Because he’s the main character of the movie

Hes also Tom Cruise

Tom Cruise isn't the last samurai though

Source?

The movie?? Just watch it, it's Ken Watanabe's character Katsumoto. The main character/protagonist of a movie and the titular character are not always the same.