Full disclosure: I'm not a web designer, but I have served as web director for multiple organizations over the years and have therefore done quite a bit of reading into design philosophy, W3C standards, and the like and have quite a bit of practical experience when it comes to the decision-making process of how to lay out a website to accomplish the goals it needs to meet.
To all the people in this thread who are insisting that the old design was "better" have an odd definition of better. It may have been easier for you because you got used to it, but speaking as someone who casually used this site for many years and only officially joined it as an active member about a year ago, I can equally insist that the old design was horribly difficult to navigate, considering it took me until only a month ago to find all the features buried beneath other pages that are now right before my eyes with just a single spacebar press or mouse click.
In terms of the design itself, while I generally prefer a combination of roll-over menus and panel menus, I feel for a site like
lichess.org which has such a large amount of features (and more coming daily), the full-screen menu overlay truly is the right decision. It's simpler to keep clean, organized, complete, and up to date. The layout Clarkey posted is not a good alternative. It's not 2005 anymore, it's 2015 and website designers need to take advantage of it. The new interface does exactly that.
I can honestly say with confidence that out of all the "issues" presented in this thread and in that other nonsense thread started by Isaiah, I only find two that are legitimately issues. The first is that the spacebar shortcut might interfere with a user's already established shortcuts. As such there simply must be a simple-to-find option to disable it. The second is the removal of the Games page. My proposed solution to that is to expand lichess TV to a channel system with multiple clocks and variants to observe, which is something I believe was already discussed awhile back. From the channels page, there could be "more games" overlay of an updated version of the central frame of the Games page in which all games of that variant/clock are being played.
Aside from these two easily solved issues, I can't honestly say there are any legitimate design problems here. It's a matter of taste, and as Thibault said, users are going to resist change no matter what you do. It was said jokingly, but there is a bit of legitimacy to what he said in regard to that fact of coding and design projects: eventually you have to just do what needs done and ignore the negative user reaction. I can say with 100% certainty that the vocal minority here in the forums doesn't represent the silent majority here who don't find any problem with the new navigation interface or even prefer it. I can also say with 100% certainty that new users to the site will find it a much simpler experience than all the users who are adapting to it now after a long period of time using the old, poorly-planned nagivation menus.