Simple sending ether to contract address works the same as calling buyWithLimit() with zero limit.

Simple sending, or payable root function defined as () in contract actually calls buy() which calls buyWithLimit like so buyWithLimit(today(), 0)

But what is really needed and NOT explained in your article - how to claim tokens and how to generate and register EOS key (without which yoo'll be unable to use tokens after EOS blockchain launch).

You should have read the article more closely. At the end of the article, it says the following.

If you need more information about contributing to the EOSCrowdsale using MyEtherWallet, you should also check out this article

Click that link. This article is specifically for contributing to a future window.