Yeah I think it tried to. You'll want to mount a folder for the C drive as well and install the program there.
Create a folder called dosgames or something like that and use the Mount command. If you created the folder in your actual C drive it'd be Mount C C:/dosgames.
Highly recommend the book “Masters of Doom” for the awesome story of John and John and ID Software. If you lived Shareware, Commander Keen, Doom, et. al, you will really enjoy this book. the book
You can purchase the DVD. It's for moments like these that I still collect physical media. I'm tired of getting shafted by media content companies who decide that they no longer feel like distributing it digitally.
Using FreeDOS instead of MSDOS tends to make things like this much easier and I can really recommend it in general. Comes with so many useful tools and improvements out of the box. Might be some obscure software that does not run, but I used it for several years now without noticing anything not being 100% MSDOS compatible.
UIDE is a disk cache. Your post is a bit lacking in details, but my crystal ball says you may not have also loaded the necessary CD/DVD driver required to grant access to said optical media.
So, under DOS, there's two bits that are required. A driver for the optical drive (there's plenty to choose from, but try vide-cdd.sys, available from https://www.hiren.info/downloads/dos-files ). Depending on your hardware, you may need to try others, but I've found vide-cdd to be pretty compatible and it has a small memory footprint.
The second part is the driver that lets DOS use CDs, which would be mscdex or, as you appear to be using, shsucdx.
Then, on top of these two, you can use UIDE.sys to cache drive reads, it uses XMS memory to do so (which means you also need an Extended Memory Manager as well).
The CD driver and uide are loaded in config.sys, mscdex/shsucdx in autoexec.bat.
Is this virtual or real hardware?
Virtual with dos box https://www.dosbox.com/wiki/IMGMOUNT
Hardware, Linux use dd with your connected drive or on there’s a plethora of image writers for Windows.
If it’s a gotek use hxc