The basic issue here is that Word has a bad default setting here, and you are assuming that Word should work correctly at the defaults. Come on, you expect them to, like, design this thing properly or something?

Sort By Paragraphs and Sort By Fields are wrong, and are poor defaults in situations where the thing you're sorting is just plain text. Following the steps you gave above, I would not have expected the sorts to work at all. In order to make it work, you have to do something else, something extra, something you didn't say you did, and something that is non-obvious in Word.

Because, according to the steps you gave, by default, Word did not have any fields to sort by. It didn't know what fields to use to sort. Instead, you have press the OPTIONS button in the sorting dialog and then tell Word what character you want to use as your column (field) delimiter.

Try this instead:

In the Sort Text dialog box, press OPTIONS.
Select SEPARATE FIELDS AT... OTHER
and in the "other" box type a space. Press OK.
Back in the main SORT TEXT dialog box, now your sorting options for your sorting columns are now available as things like "WORD 1" And "WORD 2". So now you can say Sort By Word 1, then by Word 2, then by Word 3 or whatever.

After correcting the dates to two digits with leading zeroes, then that sorts the way you would expect. For extra credit, have it sort by Word 2, then by Word 3, then by Word 4, then you get the correct date sorting without having to move the Tuesday and Friday columns.