I'll agree. OOP doesn't make a whole lot of sense here.
Representing each piece as an object doesn't make sense, but OOP is fine in terms of implementing the board itself. A class would be a good way to isolate the data and provide a standard means of observation and safe manipulation. The benefit, like frob pointed out, is that implementing in this way allows a 'player' to be more or less anything (local player, network player, AI, chicken with a USB port wired to its brain, etc).