Select whole words using single finger tap gesture
Yep!
You double-tap and lift off to select the word.  Then double-tap the selected word and start dragging immediately keeping your finger down.  It's actually kind of tricky to get to work without dragging the word but once you get it a couple of times it gets easier.
Here's an explanation on how to do it also from macworld.com, same as above:

To select text (and this works in nearly any program that involves
text) on a word-by-word basis, do a double-click-and-hold before you
start dragging, instead of a single click. As you move the mouse along
now, you’ll see that entire words are added to your selection as soon
as the cursor touches their first character. So if you’ve got a fair
bit of text to select, but still need precision, this is a pretty
quick way to get it done.

Here are my trackpad settings