Short answer, yes walk-in closets are included in the square footage. All closets in the finished portion of a home are included a home's square footage.
However, if there's a make-shift closet in a largely unfinished basement or attic, that would likely not be included in the square footage. Also, pantries, stairs, mudrooms, etc. are also included a home's square footage.
Related: Are patios included in square footage?