Most likely ruin got left behind when War was dragged back to the council (I know you don't see him during armageddon but I think war took him to earth because why wouldn't he.) and when he was waiting for war got captured the same way the Stygian did.
But atleast Stygian knows how to defy on his pathetic fate of being captured by chains. (how they capture him the first place is beyond me.) Ruin has lots of chance to beat the living !@#$ on his current master and leave him. C'mon he is not worthy enough to ride him in the first place. Only War has the right to use him. --- "Remember, kids...Chu-Chu died for your sins!"
The Stygian is one of the chosen and although captured it doesn't say for how long it could have been just a few months Ruin is a horse left alone by War from day 1 of the apocalypse so about 100 years sure he could have fought back but if he had demons would try to kill him and since the angels all hated war they would probably attack his horse also so perhaps ruin just let a demon ride him to avoid being hunted down from all sides.