Hmmm... Well you may want to actually put that on your website. And you probably want to be careful, since you've posted comments on here like "all the rest documentation can be found at Amazon S3 documentation site, it is basically the same with small differences" and you have "Amazon" on the sign, which is above the "fold" on my screen and pretty much the first connection I made on S3. If your entire website doesn't scream "we are just like Amazon S3" then I must be missing something.
you are reading that guideline incorrectly. That's a contract that gives permission to use the trademarks listed under certain conditions. That is not a guide to what amazon may claim as trademarks.
If this company had registered the "S3" trademark before Amazon had registered "Amazon S3", then this company probably could have gotten a settlement amount from Amazon... In the actual case I'd expect the company to get a C&D from Amazon at some point, with eventual negotiations being either to change the name or add a prominent header noting the lack of relation to Amazon S3.
https://aws.amazon.com/trademark-guidelines/