I think playing a game during the break (I assume video game?) would be counterproductive.

It is not at all the same as taking a "resting" break, as described in the article.

I actually have some experience here, as I have for several years played the same video game on my phone every time I go on break at work and, anecdotally, actually feel it has not helped me in this area.

I've recently decided to avoid the game except on my longer lunch breaks, and attempt to have 'restful' breaks instead. We shall see how it goes :-)