This issue is applicable to Japanese, Chinese, Korean, and Mongolian.

If you place the writing-mode property with a value of vertical-rl/lr on an individual table cell in a table that overall has a horizontal direction, you would expect the text in that cell to be displayed vertically, but in some browsers it isn't, unless the height of the td element is specified.

This appears to be because the text is wrapped character-by-character (cf. Mongolian, where words are wrapped rather than characters).

Tests & results:

Interactive test, Adding writing-mode:vertical-rl to a td element produces vertical text, with lines stacking RTL.
Interactive test, Adding writing-mode:vertical-lr to a td element produces vertical text, with lines stacking LTR.

This works as expected in Gecko and Blink browsers, as well as in legacy Edge and Internet Explorer. However, Webkit browsers, leave the text horizontal but rotate the Japanese characters to the left.

Interactive test, Adding writing-mode to a span inside a td produces the expected directionality

Wrapping the text to be made vertical in a span inside the cell, and applying writing-mode:vertical-rl to that gives the expected result in Blink, but in Safari it's necessary to also apply a height setting for the text to display properly.

Browser bug reports:
Blink • Webkit

Priority:
Correct behaviour here is a pretty basic expectation for handling directionality in tables, but since it only occurs when the direction of the td element is different from that of the overall table, this can probably be marked as advanced.

Updates:
June 2021: This gap was fixed for Blink.