Stating the "opposite colored holes don't prevent tiling by dominoes" problem requires some kind of "coloring" to know which pairs of tiles are in scope for being holes.
I agree with the comment you're replying to: the original problem (in the linked post) is about an 8x8 square in which 1x1 squares at either corner are removed, and asking whether it can be tiled by 2x1 tiles. The idea of "coloring" the board and the tiles can then be presented as part of the solution -- in fact, this is a great example of how one idea (coloring) can make a problem much earlier.
