In Word, sequential numbering will work the way you describe, whether it is a numbered list or a SEQ field. You are going to need two different list styles, one for the left side and one for the right.

If you are doing multilevel lists, you must set them up according to the instructions at
How to create numbered headings or outline numbering in Word 2007 and Word 2010.

You could set one of your lists up to match with Headings 2-5 and the other to match with headings 6-9, giving you four levels each. This all has to be set up at the same time.
Otherwise, not using a table, you could use newspaper style (snaking) columns and use a column break to start the next column. This is going to be more of a challenge to keep lined up, though.

Tables
Numbering in Microsoft Word