You don’t need to embed game rules into the matrix to solve this problem. (What does that mean anyway?) Just store the board in a 2d array of some sort and write some functions to interact with it.
That’s just not what a “data structure problem” commonly means. If it was, all programs would be data structure problems because all programs interact with data in some form.
A data structure problem is a problem where designing and implementing an appropriate data structure is in some way hard. A 2d array doesn’t fit the bill. It’s not exotic enough.