I think we all assumed here that you were trying to the firmware on a blu-ray drive in, or attached to your Mac; not a set top box for playback on your TV.
The .exe file they're talking about contains the .iso (disk image) file needed to update your blu-ray player. To avoid having to install Windows to get the self the .iso file out of the self extracting .exe, they're having you use Unarchiver to do it.
The disk image for a BDP-S300 player is
here. I selected Windows XP as the operating system, but I don't think it makes much difference since you're going to extract the .iso image from the download on your Mac.
Excerpt from Wikipedia: "An ISO image includes all the data of files contained on the archived CD/DVD, or any other disc format." Full article
here.
The bad news. I tried both the Unarchiver and Stuffit Expander. Since I have the BDP-S350, I downloaded the firmware .exe file for that, along with the one you need. The Unarchiver couldn't open the .exe files at all. Stuffit did pull something out, but it was largely incomplete. I had to extract the files with the Mac booted into Windows XP. Then put the .iso images on a flash drive to copy them to the Mac desktop.
Once you are able to get the .iso disk image out of the .exe file, you need to get that data onto a CD. Double click the .iso image to mount it. A drive icon will appear on the desktop. Launch Disk Utility , select the mounted disk image and burn the contents of the .iso image to a CD.
Once that's done, insert the CD into the blu-ray player to update its firmware.