Unable to double tap on the trackpad to highlight multiple words in macOS Mojave

I believe I figured out the difference:

Dragging:

1. Double tap and hold to begin dragging.
2. Release the mouse.
3. Depending on the amount of time that has passed, moving the mouse will do one of the following:
   • Brief delay: moving the mouse continues the dragging, essentially behaving the exact same way as drag lock. The cycle is then repeated once you release your finger.
   • Longer delay: dragging is stopped.

Dragging & Drag Lock:

1. Double tap and hold to begin dragging.
2. Release the mouse.
3. Moving the mouse will continue dragging.
4. Tap once to stop the dragging.

It's that brief delay that was throwing me off. There doesn't seem to be any way to customize the length of this delay. One thing that does help, though, is figuring out exactly how long this delay is. One method for figuring this out is the following:

1. Drag an icon from the dock a tiny bit so that if you were to release it, it wouldn't be deleted.
2. Release the mouse.
3. Observe how long it takes for the icon to move back to its place. That is the exact amount of minimum time that you should wait when you are finished dragging something.

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