In Saito's commentary to "Budo" he correctly notes that O-Sensei used "six-directions" and not "hanmi" or "60 degrees", but he speculates that this is because O-Sensei did not use the term "hanmi" at that time budo was written (for some reason unspecified by Saito).
My personal hunch is that it's one of those things that O-Sensei dropped because nobody understood what he was talking about and he didn't care to explain - for all that he broke with Takeda it seems to me that he was somewhat cagey about stating some things explicitly in clear language. Many times it seems that he expected (or wanted to see) people following the hints he dropped - also a common traditional tactic. "Stealing the techniques", in other words.
I want to note that, in reading Saito's Japanese text, it appears to me that he was unaware if there was a reason for the change in nomenclature.