Well, I'm afraid that you will have to purchase a commercial licence if you intend to sell programmed PicAxe chips included in your design.
The "The Programming Editor software is free to educational and home users (non-commercial use)" is a little confusing, and I also read it that commercial users would not be able to use the Programming Editor for free but would need to pay for some sort of license. That's not correct - See Technical's response in ...
http://www.picaxeforum.co.uk/showthread.php?t=597&highlight=commercial+product
What do I do if I want to sell devices with the picaxe chip in them?
There are no restrictions or royalties requested for PICAXE's used in commercial products and you don't need any licence to undertake commercial development or use teh Programing Editor to create programs for use in commercial products. As long as you are not shipping the Programming Editor with your product there are no obstacles.
You'll need product liability cover, certification and so on for a PICAXE-based product just as you would with any product, but that's the business side of things. The PICAXE is used in commercial product but Rev-Ed will not supply details of their commercial customers.
The only think I would ask is that if asking for help on a commercial product in the forums you are up-front about that. Firstly it helps people judge the 'skill level' a response can be targeted at, and it's only fair to let people know that their free help is being used to make you a profit. It's only fair to let them decide how much help they are willing to give. PICAXE usage help will always be forthcoming and product design help has been given to other commercial users. As long as you aren't looking to rip people off by getting your code written for free, you should find a lot of help.