It appears to be little clips holding it in place, that pass through slots in the acrylic and just bend over to secure it, judging by this part of this case-modding video where they appear to be reinstalling the original acrylic panel after painting the case...
https://youtu.be/U2XR6A-Fw1w?t=394
If you decided to replace it with a self-cut panel though, it might be hard to accurately cut those slots, so you might want to bend over the clips and use something like epoxy to secure the panel in place, or maybe even hot glue if the panel is lightweight enough. Note that they also cut some acrylic earlier in that video after using tape to mask it off, though not for a side panel. They use a table saw, but it should also be possible to...