OK, this sounds like a simple matter of copying your exported file to an SD card, just like you would to any other USb thumb drive or a floppy back in the day.
1) Figure out the exact specs the WD player needs for the 1080 file. Codec, bitrate, etc.
2) Make a new setting in Compressor with those specs
3) Export a SCQT from Final Cut Pro and drop into Compressor; use the setting you made for the WD player
4) Mount an SD card on your desktop -- you have a new iMac with the slot, right? If not, use a USB adapter. The card should appear on your desktop.
5) Drag your compressed 1080 file to the card. Eject it and try it on the WD device to make sure it works.
That should do it, unless I'm missing something...
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SCQT! Self-contained QuickTime ? pass it on!