Is there really a Nash equilibrium in this example?
The Nash equilibrium is indeed (down, right).
Note that your chart has helpfully underlined the max value among all possible strategies each player can play, conditional on what the other player plays. The steps on the graph  are useful as well: If no numbers are underlined in a cell, that strategy set is strictly dominated by something else. If one number is underlined, one player will want to unilaterally deviate.
Assume the players play (down, right):

P1 will not want to play up or center as their return will be 1 in those cases
P2 will not want to play left or middle as their return will be 1 in those cases

You can try this for any other cell with underlined values and see one player will be better off deviating. For example, in (up, middle) P2 would prefer to deviate to (up, left), then P1 would deviate to (center, left), P2 to (center, middle), P1 to (middle, up), etc.
FYI: the equilibrium should be referred to by its strategy rather than its values.