That is the context menu for the cell contents that comes up when I right click on the text in Word 2007. The W2007 designer looks quite different from your image. Maybe that context menu is deprecated in W16 but I doubt it.
Try this:
Select the cell/s you want to align.
Ribbon > TableTools > Layout > Alignment section
There is a patch with nine icons. Hover over them to see the description and click the one you prefer.