The root cause of your problem seems to be that you tried to uninstall python-requests, which is a requirement for My OSMC which is in turn a requirement for Kodi, so this caused Kodi to get uninstalled:
Removing rbp2-device-osmc (1.2.9) ...
WARNING: You have tried to remove a package that is essential to OSMC's operation.
To undo these changes, run 'sudo apt-get -f install'.
dpkg: error processing package rbp2-device-osmc (--remove):
subprocess installed pre-removal script returned error exit status 1
Removing python-pip (1.5.6-5) ...
dpkg: python-requests: dependency problems, but removing anyway as you requested:
mediacenter-addon-osmc depends on python-requests.
Removing python-requests (2.4.3-6) ...
dpkg: ca-certificates: dependency problems, but removing anyway as you requested:
armv7-network-osmc depends on ca-certificates.
Removing ca-certificates (20141019+deb8u1) ...
Removing dangling symlinks from /etc/ssl/certs... done.
Removing openssl (1.0.1k-3+deb8u4) ...
dpkg: armv7-network-osmc: dependency problems, but removing anyway as you requested:
rbp2-device-osmc depends on armv7-network-osmc.
Removing armv7-network-osmc (1.6.1) ...
WARNING: You have tried to remove a package that is essential to OSMC's operation.
To undo these changes, run 'sudo apt-get -f install'.
dpkg: error processing package armv7-network-osmc (--remove):
subprocess installed pre-removal script returned error exit status 1
dpkg: rbp2-mediacenter-osmc: dependency problems, but removing anyway as you requested:
rbp2-device-osmc depends on rbp2-mediacenter-osmc.
Removing rbp2-mediacenter-osmc (16.0.0-1) ...
It looks like you ran the command to reinstall rbp2-device-osmc, and mediacenter-osmc is re-installed, so the issue is probably just that the mediacenter service is no longer enabled on boot. So just do:
sudo systemctl enable mediacenter
reboot