I think the story is pretty explicit that the pieces are mindless. They get into it a lot in episode 6, especially with the scene of Battler talking to piece Beatrice.
That said I don’t think them being pieces invalidates them in any way. It’s all about perspective.
On the board itself they are people. From the perspective of the players on the meta level they are mere pieces. However on the level above that they are merely part of a story being written by Yasy/ Hachijou Toyha. And on the level above that even those characters are simply part of Ryukishi’s story that we are reading.
The pieces are just as valid as any other fictional character. Just because they are several levels deep does not make them any less of characters. The restriction that they can only perform actions they specialize in helps with that as well. It keeps them consistent as characters despite changes of GMs.
That said there is still a distinction that must be made between piece-meta- and “real” versions. For example piece Kinzo changes a lot from game to game because his range of acceptable actions is rather wide. His presence is often larger than life and this is because of how his family and the world in general view the mysterious Kinzo. We don’t get to see what “real” Kinzo was like, but Battler reminds the viewers in episode 8 that what we did see was only an interpretation of Kinzo.
That’s why when viewing any character in the story it’s important to consider them from all angles, how they are presented in all stories. Things that change between different GMs or different authors as well as things that stay the same are clues that lead to a clearer view of the actual person.