The mode 2 output looks very odd - the space values are oddly large. So I'm not 100% sure if there might be some problem with IR reception - or maybe the batteries of the remote are flat and it's not working properly?
I'm not familiar with the original xbox remote, but if ir-keytable configuration doesn't work you could try the lircd.conf files from here: lirc-remotes / Code / [395780] /remotes/microsoft
This one looks like it could work: xbox.lircd.conf?format=raw
Download the file and copy it to /storage/.config/lircd.conf, then reboot (LE9.0 preview builds will automatically pick the file up and run lirc, in LE 8.2 you have to enable Lirc in LE settings).
But before doing that I'd check into the mode2 output, the pulse/space values should usually be about 400-2000.
so long,
Hias