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It's a math based puzzle commonly known as Sudoku, the rules are that each 3x3 square can only have numbers 1-9 with no repeats, same with each 9x1 row or column. A set of numbers are placed as a starter pattern (you can solve from blank but it's significantly more challenging) and you need to fill in the remaining numbers.
It's a logic puzzle, no math is involved. It used numbers but those could be replaced with the letters 'A' through 'I' and function the same. Otherwise correct.
I started typing an angry comment about how math is logic and therefore sudoku is a math puzzle, but when I got to the second paragraph about graph theory I realized I was already losing the argument I was having with no one
Math is more than just numbers and arithmetic. There's even a Wikipedia page dedicated to the Mathematics of Sudoku.
Mathematics can be used to study Sudoku puzzles to answer questions such as "How many filled Sudoku grids are there?", "What is the minimal number of clues in a valid puzzle?" and "In what ways can Sudoku grids be symmetric?" through the use of combinatorics and group theory.
That's completely different from a Sudoku puzzle itself or the process of solving one.
Sure, it's math in the way that everything can be described using math, but you wouldn't explain 'purple' as "the math of calculating what volume of blue to add to a given volume of red in order to reach the desired hue."