From the Wikipedia Page
Duty-free shops (or stores) are retail outlets that are exempt from the payment of certain local or national taxes and duties, on the requirement that the goods sold will be sold to travelers who will take them out of the country. Which products can be sold duty-free vary by jurisdiction, as well as how they can be sold, and the process of calculating the duty or refund the duty component.
So what the exemption means vary from country to country and is based on the laws of that country and administrative divisions within the country.
What does it imply in terms of prices? May not be much, for example Alcohol prices in Duty Free Shops in the US may be more expensive then some of the prices on the same Alcohol in a different locality. Tobacco Products may be less expensive then some jurisdictions but more expensive then others and so on. Reasons for that vary but the situation you saw in Doha is entirely reasonable.