I have no (major) problem reading it online, but it just wont let me. If i go to your link, i am sent back to the kindle store. Then if i try to 'buy', i am required to have a kindle serial number, there is no other way to proceed. (I assume if gives you an ID or something if you download the app, but there is no 'read online without a kindle' choice).
It worked for me with my existing Amazon account, but then I have a Kindle.
I thought I'd test with a new account, so in an incognito window:
* Went to https://read.amazon.com/
* Created a new account
* Got redirected to Kindle store, found free book, hit "Buy now with 1-Click"
* Filled in a billing address
* Got a page thanking me for my order, hit "Read now in Kindle Cloud Reader"
* Book loaded
You're welcome to use this account--login: "M8R-2neeuu@mailinator.com", password "test123".
This will let you read it online. It looks like there's some offline support but I haven't tried it myself.