Ever since Electronic Arts' Origin stopped counting non-Origin, non-Steam gameplay time early last year, I had moved the shortcuts for those games to Steam. I waited for a long time for them to fix this problem but after checking for one last time on June 24th of last year, I just gave up and had forgotten about the situation. When I suddenly recalled about the issue today, I decided to add League of Legends back to Origin to see if EA finally did the right thing and to my surprise, they did! So I am moving these games back to Origin since I don't know why Steam still doesn't have this feature implemented to the Steam client. Welcome back to my good graces, Origin! You started 2015 off on a good note!
The previous accumulated time of 800+ hours is gone but at least the feature is back!