Take this with a grain of salt from a non-programmer, but I don't see it possible with the current version of ScummVM or DOSBox. I can't imagine there's any code to both program and take advantage of an FPGA chip. So as far as either program is concerned, it doesn't know the FPGA chip exists nor what it would even do with it. Hardware rendering leverages a computer's GPU to help with emulation rather than usually strictly CPU in software rendering so I'm guessing you mean for the FPGA to recreate a GPU. That's a bit of a tall order.
Let's say someone did branch off ScummVM or DOSBox to be able to code an FPGA chip. What would it be able to bring to the table in the DE10-Nano? It's hitting a ceiling with PS1 and Saturn era hardware so nothing too modern would fit. I don't know what kind of GPU could fit into the programmable units of the DE10-Nano. That's also assuming the full board of the chosen GPU has documentation to outline every chip and trace in order to recreate it. Otherwise, someone would have to do that work first. On top of that, someone would also have to figure out how to get the ARM CPU and the recreated GPU to communicate without issues. And after all of that there's the golden questions of the hour: would it improve anything?
From where I'm seeing it, basically the entire premise would be starting at square one. That's a lot of work that would have to be done to try to add hardware rending for one device. And that's me assuming there isn't a process I'm overlooking as an outsider that kills the whole theoretical in the first place. If you're feeling brave, then by all means go for it and see how it works out. But otherwise, I think this is just one of those things best left to the less specialty boards.