It can be done using a rooted Nexus 7 2013 with the "stickmount" app.

The 810 looks like a USB stick to the computer you attach it to. Maybe, look up how other people use USB sticks on your tablet.

If your tablet has a microSD card reader, you might be able to put the card from the 810 into the tablet and write the files to it that way.

It looks like it should work simply.

You have to copy the files from the tablet to the location (directory/folder) that the attached USB stick/Garmin shows up in the file system (it might not be obvious where that is).