Most steps are just per the video. First insert table with one raw and 2 columns, and adjust the width of the right column like this:
If you want formulas to be exactly centered on the page, you can optionally insert 3rd column on the left with the same width as the right column. Type parenthesis in the right column and click inside them. Then click Insert--->Quick Parts --->Field. Scroll down to StyleRef. You will get a menu like you see below.
Check Insert paragraph number in the Field options, and under Style name select the section which you want to be the base of the numbering. If, for example, your chapters are based on Heading 1, select it in Style name. When you hit OK, it will print the number of the current "Heading 1" chapter. Then type period (dot) and click again Insert--->Quick Parts --->Field. This time scroll down to Seq (which is sequence field). Add a name to this sequence, for example Seq eq.
When you hit OK it will print the number 1. In our example, if you do it in the Chapter 1, the result in right column will look like (1.1). Every time you repeat this procedure the numbers will automatically update sequentially. Optionally, you can click in the main column and then click Insert--->Equation. This will place an equation placeholder there. Finally, select the entire table and get rid of borders.
To simplify the process so that you won’t have to repeat it manually every time you insert a math formula, you can save all this as an auto text. Select entire table and click Quick Parts--->Auto text--->Save the selection in auto text gallery. When you will need to place the next formula, you will just go Quick Parts--->Auto text and select your saved auto text. This method will likely work in Word 2013, although I did not try it.
By the way, Equation Editor is an optional component of MS Word. You need to select it when you first install Word.