If the @vanfog 's steps didn’t work for you, like in my case (stuck in “Installing file…”) You can try followings. It takes extra time but it is technically more correct to not do “dd” on the same file system where linux is running.
1.) run osmc installer and prepare USB version with .img file: 2015.10-2-USB
2.) boot from USB and let finish osmc installation on the USB stick.
3.) ssh to apple tv (user:osmc pw: osmc)
4.) run following commands one by one:
cd /home/osmc/
wget http://download.osmc.tv/installers/diskimages/OSMC_TGT_appletv_20151123-HDD.img.gz
gzip -d OSMC_TGT_appletv_20151123-HDD.img.gz
sudo dd if=OSMC_TGT_appletv_20151123-HDD.img of=/dev/sda bs=4M
NOTE:to download HDD.img file image you need also internet connection for your appletv
5.) remove USB stick and reboot appletv
6.) wait untill installation from HDD is finished
7.) extra hard reset might be needed if “appletv ?” will appear
8.) done 