Fair enough. I'm also having issues with audio breaking up and slow gameplay. Chrome Win 7 here too. It sucks, but it's not that bad in context.
Sure, there are some technical issues behind this, mainly because the operating system these games work on no longer exists on actual hardware (or at least, it's quite rare). Instead an emulator (DosBox) is being used. However DosBox itself was written to run directly on your OS. Take that functionality, recompile it into JavaScript, and run it in a browser, and you're bound to bump into some issues.
From a technical point of view, these glitches are nothing time and effort can't fix. Consider though that despite the glitches, your web browser is able to run software from the 80's and 90's and fool that software into thinking it's running natively on a PC of the day. These aren't web re-writes, these are the actual programs packaged to run in your browser, as if your browser itself is the PC. It's really quite impressive.
Consider any assembly instruction an old DOS program might have made, such as directly accessing VGA ram in the A000 range (mode 13h for the win!), and this browser implementation is able to translate it to pixels on "screen". The only other way to run these games is to go and find a working 386 or 486 with DOS.
For the mouse glitching, because these games were written for a totally different era, in which controls like mice were not mandatory (many people didn't own a mouse until well into the 90's), and in which there were no standard driver libraries shared among vendors, the control schemes were often rolled out on a per-project basis, with each developer building their own version. Developers working with mice often had to deal with actual binary pulses on serial ports rather than pixel coordinates provided by layers of abstraction, so they would often interpret these however suited their project. It's not a surprise that the modern Windows 7 cursor doesn't line up with the game's interpretation of the cursor. Nothing short of rewriting the game's cursor routines or creating a mapping algorithm for each game would fix that.
Despite the number of obvious improvements that can be made, I think the main point is not to have a fully working in-browser gaming arcade, though fixing a lot of these problems would be super sweet. Instead I think this is significant because this is software that could literally disappear from human history if not for these efforts to preserve it, as dramatic as that sounds.
It may seem trite and, in today's implementation somewhat buggy, but the fact it will be around for generations to come I think is an important part of preserving even this tiny piece of human culture. People kept a bunch of oil paintings and songs from hundreds of years ago as examples of the primary motivators in various disciplines, so why not preserve early gaming history?
In these archives you will see examples of the first three dimensional first person shooters, the first space trading games, the first side scrolling action games, the first of the elder scrolls games, fighting games, etc.
As trivial as it seems these programs are a real piece of history that impacted popular culture, and the actual hardware that used to be able to run them is obsolete and hard to come by.
So I hope this answers your first question "What am I missing?", and for your second question, yes, it could use more work. But this is a great place to start.
Sorry for the long post, hope it made sense in some way and put some context around why people think this is great.