The statement from his wife simply says he went for a walk. Presumably she knows more about where he intended to go. But the only two possibilities now appear to be that he planned to walk to/via the peninsula beach (Agia Marina) or over the peninsula and into Symi that way
The impression given is that he/they weren't communicating much with each other.
Or she knows more and it's not being shared.
It's hard to believe he just said he was going for a walk and didn't say how long he'd be, and where they'd meet up.
Most people say where they are going, how long they'll be and where they will meet .
And then there's the confusion that he was 'tired' which became 'feeling unwell'.
I don't know if that came from his wife as there's so much poor and contradictory reporting.