If you read the text on the download page, the bit where it says "For all other downloads (files to use with 3rd party SD creator tools, manual update files, NAND install files, noobs files, files to migrate you from OpenELEC, etc.) please select your hardware in the drop-list below:" .. and then click in the drop list you can navigate away from the Raspberry Pi downloads to the Generic AMD/Intel/nVidia image downloads.
To recover an existing installation either create a new LE USB and attach a keyboard, then boot from the USB and CTRL+ALT+F3 to access a local console where you can mount the internal drive and download/extract/replace the KERNEL/SYSTEM files in the boot partition. Or create an Ubuntu LiveUSB and use GUI tools there to do the same thing.
NB: LE has mechanisms to detect and abort updates when people load the wrong files, but when you first update from OE you're using OE's older update process and this has no protection.