dtgreene: Also, why does the client need to be so big?
Ah, that's an easy one. Galaxy client like the majority of mainstream gaming clients is based on web based technologies, which makes sense because it intends to be a frontend for the store and majority of the GOG website functionality. So essentially it is a special purpose modern web browser that must be compatible with all of the current web technologies that GOG intends to use on their website. Instead of writing their own web browser from the ground up to do this which would take many years to end up with more or less the same result at great expense, they chose the more sensible decision to use existing freely available technology to do the same thing - namely Google Chromium. Google Chromium is the open source portion of the Google Chrome web browser, and full blown modern web browsers are fair sized applications which have a variety of dependencies themselves on various 3rd party libraries and other dependencies. All of these things must be present for the browser to work, and are thus an included part of it. In addition the user interface graphics and other data are necessary for it to work properly.
The Chromium engine itself (libcef.dll) can be found in your Galaxy client directory and if you have a look you'll see that it is approximately 52 megabytes in size. If one has a look at a fresh installation of the Google Chrome web browser itself, it is a few hundred megabytes in size altogether including all of the DLLs, data etc. Galaxy is actually Google Chrome on a severe calorie restricted diet in a sense, gaining all of the necessary functionality GOG needs for their client without the extra unnecessary bits. The fact is that web browsers are large complex applications, and so applications that are based upon web browser technologies are also large complex applications.
So the reason why it is as large as it is, is because for the type of functionality that GOG wants to provide in their gaming client, in terms of features, usability, the resources needed to build such an app, web based technologies are the best solution to build it with and reusing existing freely available code to do so rather than spending years developing your own code to do the same thing is what is most economically viable and expedient to develop with.
dtgreene: A functional Linux distribution, complete with a GUI, can fit in only 16MB, for example. (Actually 12, but even the distro I'm thinking of has grown over the years.)
Yes, for a very minimal definition of functional which doesn't really include being a full blown video game client for a modern gaming distribution platform. Not really a useful comparison by any stretch. Plus, I wasn't present during Galaxy design meetings or anything like that of course but my gut feeling tells me that fitting the client on a floppy disk to run off of a 16MB Linux distribution was not one of their design goals. :) Maybe if they used a DeLorean and went back in time to say... 1993 that might have been how the meeting went. Galaxy might very well have been based on the "lynx" web browser by that measure. :oP
dtgreene: In fact, back in the day, we had entire games that could fit on a handful of floppy disks, sometimes even only one.
Indeed, and we still do. They're not capable of providing the feature rich full blown experience of a modern gaming client either though. If they were, they wouldn't fit on a handful of floppy disks unless one has really large and very strong hands. :)
Technology evolves, it gets more capable to do more things over time and so people design more complex software that does more things. Computers double in computing power and storage capacity roughly every 18 months, and software takes advantage of what the new capabilities of the hardware is and gradually increases in size as a result of doing more and providing more features and functionality and conveniences to us in our daily lives. It's essentially a natural part of technological evolution and there's nothing inherently wrong with that.
Atari 2600 cartridges by design held a maximum of about 4kB of ROM on them (without special hacks). That was my first home gaming system. One could compare Pitfall to The Witcher 3 and say "Why does The Witcher 3 have to be so huge at 40GB+ in size? Why couldn't they make it 4kB like Atari was able to in 1981?" Well, they could... but it wouldn't be the same game nor provide the same features, functionality, conveniences nor overall experience to the potential customer as the 40GB+ game does either. It would end up being more like Atari "Adventure", which did fit in a 4kB cartridge I'll give you that, but it was no The Witcher 3 either.
I'll gladly offer up a metaphorical red carpet 50GB of hard disk space dedicated to Galaxy if it does what I want it to do, and that's not including space for games or other content, just the program itself. That might seem huge and by various measures it is, but 50GB means absolutely nothing to me if an app wants to use it. As long as it gives me an experience that is worth 50GB or 10GB or 1GB or 100MB or 1TB or whatever, then I'm not too concerned how much space it takes to do that personally. I don't expect everyone to feel the same way, but people can still run Atari 2600 games if they want to too, or play floppy disk based games on the 16MB Linux distribution you're referring to.
There's something out there to float everyone's boat! :)