Choosing a game for a two-minute break
If one level does not finish before the queue ends, the game is in the wrong slot. Pick one with short levels that saves progress.
If one level does not finish before the queue ends, the game is in the wrong slot, not the wrong game. For a short break, the two things worth checking are not genre but level length and whether progress is saved.
A title with three-minute levels suits a queue, but only if the board survives the tab being closed. If it does not, you replay the first level every time you open it, and that is not a rest, it is extra work.
For a genuinely short break, pick something you can leave mid-level without losing anything. For a thirty-minute gap, pick a single long level instead, because reloading five short ones costs more time than one continuous session.
Also check whether the page saves your position when the tab closes, not just whether the score is kept. Plenty of titles keep a high score but restart the level, which stretches a two-minute break into ten.
If you keep many tabs open, launch the game in a new tab and leave the work tab where it is. Games that reload when a tab becomes active again will wipe progress that was never saved.