It is just an expression to add enthusiasm. It isn't to mean that
  other existing web services architecture aren't build for the web.
Since REST is a choice implementation for a lot of lightweight(not much extra xml markup, human readable, no toolkits required to build) requirement, it has gotten a lot of traction in the past few years. Articles and papers reflect that enthusiasm by making statement that sound like Universal Truth but just know that they are trying to add a hint of enthusiasm. It also doesn't mean SOAP isn't used equally. SOAP is also built for the web. 
They both have advantages and disadvantages. Other members on this site have given good accounts on the same. Here are good pointers on which one is used for what.
Which Web Service?
SOAP vs. REST