It definitly had to do everything with Web, it was the agreement between Mozila going with asm.js, Chrome pushing for PNaCL, Adobe with CrossBridge, Sun with Java, Microsoft with ActiveX,....

Then some folks rediscovered UNCOL from 1958, all the systems influenced by it, and started to sell the dream of the bytecode that was going to save the world.

This is retconning the history of WASM. While WASM was designed to be also be usable outside browsers, nobody could really predict at the time what this usage would look like exactly.

That's were it came from but it's perfectly able to run in environments that don't have anything to do with the web.