First check the easy test and watch it fail. Middle is not beaten by Top alone: against Right, Middle pays $1$ and Top pays $0$. It is not beaten by Bottom alone either: against Left, Middle pays $1$ and Bottom pays $0$. So no single row of yours dominates it, and a domination test that looks only at pure strategies keeps Middle.

Now allow a mix. Play Top and Bottom with probability $\tfrac12$ each. Against Left it pays $\tfrac12(4) + \tfrac12(0) = 2$; against Centre, $\tfrac12(3) + \tfrac12(3) = 3$; against Right, $\tfrac12(0) + \tfrac12(4) = 2$. Every one of those beats Middle’s flat $1$, so the mix strictly dominates Middle and no belief about the other player can make Middle a best reply. Delete it.

Faded. Suppose Middle paid $2.5$ in all three columns instead of $1$. The same fifty-fifty mix now pays $2$, $3$, $2$: it no longer beats Middle everywhere. Look for a belief that makes Middle best: put probability $\tfrac12$ on Left and $\tfrac12$ on Right, and Top pays $2$, Bottom pays $2$, Middle pays $2.5$. Middle survives, because a strategy that is mediocre everywhere is the right hedge against a genuinely uncertain opponent.

Solo. Back to the original numbers, and now run the same test on the other player. Their Centre column pays them $1$ whatever you do, exactly mirroring your Middle. A fifty-fifty mix of Left and Right pays them $2$ against Top and $2$ against Bottom, so Centre is never their best reply either and it goes too. What survives on both sides is Top and Bottom against Left and Right: the rationalizable set of this game.