There are a couple of reasons you might need to merge words together.
1. The words needing to be merged are meant to be a single word. i.e. Clipscribe as in the example in the video.
In this case, you want to use the button in the word pop-up options which will merge the two words into one removing the space in between them.
2. Or, you might want the words to be styled as if they were a single word, so in this case, you would use the button which will merge the two words and keep the space, but the two words will be treated as a single word for Substyling purposes.
When using the word-by-word display, and you merge two words together, they will have the same timestamp and show at the same time.
In either case, you can either Shift-Click the two words to select them first or drag-select them. Then click on of the merge icons to merge them.