I think the "Just Play" button on the Please Log In screen is very difficult to notice. I bet most users won't notice and will instead close the page without reading all of the modal dialog.
It is large and same shape as buttons for other options. Plenty of websites that try to hide least desirable options (for them) by making them smaller and assigning a style that doesn't look like a button at all.
The color is slightly different from options. That has both benefits and downsides. One hand it helps it to standout, on the other hand it can cause you not to consider as an option. Although I personally think that it would be more hidden if it had the same color and it was placed in the middle of list with rest of login options.
I guess this demonstrates how many bad websites have trained people to ignore popups so that they instinctively close them or whole website in a fraction of a second, or if they don't instantly close it brain blocks the ability to perceive any information within the popup.
Did any of you had the later experience where you spend some time looking at the login screen for a while but weren't able to perceive what's in front of you? No need to answer if it was the first case. There is very little you could perceive within the short time it takes for some of you to close it.
For me personally it wasn't that bad. There was something like a half a second hiccup, where I thought that this is will be one of those sites that want you to login, but was afterwards pleasantly surprised that they offer option to play without logging in.
The issue is that it is at the end of a list of login options and looks similar to them. Why would I read the login options when I have no interest in logging in?
One solution that comes to mind would be a modal with two columns. One column for the login options and the other for the just play button.