One would guess that
text-align: center itself would do the job, but because the promoted links have a modified
display-attribute, they no longer conform to
display: block, which takes all the available space and respects the styling of
center. However, by changing back to
display: block, the functionality still works so it's alright to add it to the code.
The following does the job:
If you only want to apply the changes to the body text, you need to have
.ms-tileview-tile-descriptionMedium on the selected elements, and vice versa.