First of all, if I were to find a copy of the IPA file online, would that be considered piracy?
It won't constitute piracy, primarily because the iOS App Store ecosystem has been designed from the ground up to curb attempts at pirating apps. Even if you manage to find the IPA of the said app, you won't be able to load it on an iOS device. Side-loading app like in Android is not generally possibly in iOS.
Secondly, assuming such activity is not illegal, are there libraries that .IPAs of ancient iOS apps?
No. There isn't any such library/website which will let you download the IPA file for desired app.
Your best bet would be search the Web for reviews/videos of the game app in action. That way you would be able to study the design at-least in a limited/indirect way.
Additionally, considering the app was discontinued around 2012 which were the days of iOS 6/iOS 7, it's highly likely that the app was developed using a now ancient iOS SDK and using older 32-bit architecture. Even if we hypothetically assume that you'll be somehow able to get hold of the IPA and load it on a device, it won't be possible to run in on a modern device (running iOS 11 or later), which is now installed on around 95% of active devices.
Source: App Store - Support - Apple Developer as on 10 April 2019.
P.S.: Quoting @Tetsujin from the comment below:
If it's that old & has been unsupported for 6 or 7 years, it might even be worth seeing if the original dev would be willing to give away the old source code. It's obviously something they're not currently making money out of. You never know, it might just happen.