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

I'd try using the three finger dragging method. In the Trackpad System Preference, set Three Fingers to Dragging. Double-tap a word to select it, then use three fingers to drag from that word to highlight more words.

Double tap this word. Then hold shift and double tap this word.