Well you kind of nailed it right on the head. Just to note that I do have a Bachelor's in CIS with an emphasis on Networking and Network Security.
This is the exact specification of a DoS attack. Thousands of users all hitting a server simultaneously and bogging it down with more requests per second than it could handle. Typically this is an automated type of attack, otherwise known as a DDoS run with a botnet, but it has been seen that popular services can easily become overwhelmed by traffic just like this.
For those of us in the field, a term you might often hear is about a website being 'Slashdotted'. This, however, is in no way a sophisticated term and instead refers to a popular techie site known as 'Slashdot.org' which hosts a lot of stories about relevant (and sometimes irrelevant) techie news. Sometimes stories get put up on their with links to other sites and so many people go to view the linked page that the site gets overtaken by all the traffic.
This means being 'Slashdotted' is a double-edged sword. Firstly it means that the material you're presenting is hugely popular and everyone wants to see it now... a good position to be in. The other side is that you're so buried in people trying to get their hand in the door that no one can fit.
There's only two solutions to the problem.... shut down the service and try again later... or add capacity. Option B is obviously the better of the two, but remember that adding capacity for their servers means a LOT of downtime, both in physical setup and logical configuration.
Now granted, this should have been noticed and taken care of after OB, but they were struggling on other issues as well. Realistically, OB should have been much much sooner than it was, giving them time to not only test well but act on the results of that test. A good rule of thumb they should have followed... take the number of users logged in before the service started having issues... multiply that by five... plan for that.