While Minotaur Reckoner is on the board, can a unit move to a base through any other effect apart from its own move effect, e.g. with a Ride the Wind spell?

No — while Minotaur Reckoner is on the board, no unit can Move to base by any means, including spells like Ride the Wind. Its ability "Units can't move to base" is a blanket restriction on the Move action, not just the Standard Move.

The spell or ability still resolves, but the move instruction simply fails — per Rule 359.3.e.6, instructions that can't be followed are ignored (FAQ #8815).

One caveat: Recalls are not Moves (Rule 451), so effects that recall a unit to base would still work. But any effect that literally says "move to base" — Ride the Wind, Tideturner, Reaver's Row, etc. — is prevented.