Do all units currently on the board become ready when I play Magma Wurm?

No. Magma Wurm's ability reads "Other friendly units enter ready" — it modifies how future units arrive, not the state of units already on the board.

The ability is a passive modifier that applies when another friendly unit enters the battlefield, not a retroactive readying effect. Any friendly unit already on the board when Magma Wurm comes into play stays in whatever state it's in (exhausted or ready). If you want to ready existing units, you'd need a different card or effect that specifically says "ready" — this one only affects the entry state of units played after Magma Wurm.