It is free for the uses outlined in the top section in your "Web Mapping Pricing" link:
- Development and Evaluations
- Non-commercial external use
- Education(teaching purposes only)
- NGO or not-for-profit business
- When used in conjunction with ArcGIS for Server license
- When used in conjunction with ArcGIS Online Task Services totaling $4,000 per year or more
For commercial use, on a publicly accessible website, it is not free. That's when you need to contact sales for a quote.
Edit: best source for this info as of December 2013 is https://developers.arcgis.com/en/terms/