This is good to know that we can win Sudoku with a computer program but not surprising.
The goal of Sudoku is to make your intellect work and find logic by yourself. The article should be named: How to win every Sudoku puzzle by cheating.
What's better for the brain, solving Sudokus, or writing a Sudoku solver?
Both can be good. Chances are that your first Sudoku solver uses some bruteforce approach, while your manual solution certainly does not. Then the intuitions that you get from many manual games can drive the design of your solver. Of course you can implement some established algorithm but I don't see that challenging.
I have mathematician friend who won't ever play Nine Men's Morris because it's a solved game, so it's not longer interesting for him. It's a shame, you can learn a lot even playing Nim variants if you don't already know the winning strategy, it's a good learning material for kids too.
Instead, as you suggest, staving off cognitive decline might be better accomplished by learning some Python, learning a new language well enough to do some traveling or reading with it, learning to play a new musical instrument, learning some simple juggling, or whatever is both safe and more cognitively taxing than polishing an existing skill by repetition.