Just tried it on an XP VirtualBox VM. Still broken. :(

The thing about Windows 95 (and every other version of Windows before ME for that matter), is that it's just a ui program that runs on top of DOS . Anything that runs within Win 95 should by extension be compatible inside an accurate DOS emulator. This is why I said I might question it.
Though now that I think about it, there is the aspect that you have to actually have access to a copy of windows to install it in DOSBox.

Did you run VirtualBox with 3D support? It's off by default.
You need to enable it in the VM settings and then install the Guest Additions' 3D support while running the guest OS in Safe Mode. You will probably also need to install DirectX 9.

That's more an urban legend than the real deal with Windows 95 :-P The DOS portion of Windows 95 is mostly used to boot the PC and take it to the 32-bit protected mode, where the kernel manages I/O and low-level interfaces (drivers, later DirectX and other common abstractions) with peripherals.
DOSBox is clearly unsuitable for all this, because it's main purpose is to emulate as accurately as possible DOS interrupts, specific hardware peripherals and this kind of stuff. Imho there's the need for a completely different approach to manage a project like a Windows emulator to hope to get quality results that are comparable to DOSBox.
All this besides the fact that "Windows emulation" is bullshit because you can't possibly emulate 500 Megabytes of system files & utilities if you don't want be called "React OS". Which is not a virtual machine but an OS on its own :-P

I never got as far as launching a mission, so I don't know if I missed a step in the 3D setup or not. First thing I checked was Ghost Bear's mech lab, which still gives a bogus "Keshik defined maximum tonnage exceeded" error when you try and use a customized mech.

Depends on the game. Wine does have support for 16 bit applications, but like everything run in Wine, the functionality provided by that support can vary by application. Wine's Application Database could tell you if a specific game can be run through Wine.

And I guess that's why "Wine Is Not an Emulator"....