After King Demavend's death, Prince Stennis became heir to the Aedirnian throne, at least in name. However, pride and a chilly disposition rarely win the love of one's subjects, and that was very much Stennis' problem. His youth did not strengthen his claim either. Though no one openly questioned the Prince's claim to the crown, Stennis did not have enough support to actually have it placed upon his head. Given this situation, sitting out important events would have been political suicide. The war for the Pontar Valley gave him the ideal chance to bolster his position by demonstrating what a good ruler he would make. History has shown time and time again that when a realm is in chaos, deeds rather than words grant one legitimacy in the eyes of one's subjects.
Stennis greatly desired to prove himself the equal – or superior – of the Virgin of Aedirn. He had strong support from the nobility, yet the common folk had few reasons to sympathize with him.
If Geralt chooses Roche's path during the end of chapter I:
He was not lucky enough to leave the ghastly battlefield in one piece. Thus the Aedernian throne was left without a legal heir.
If Geralt chooses Iorveth's path during the end of chapter I:
His refusal to help Saskia said much about the youth's personality – none of it good.
When he got involved in the conspiracy against Saskia, the young prince forgot that crowned heads fall as easily as those of serfs. He was found guilty as an accessory to the assassination attempt and paid for it with his life.
If Geralt does not find him guilty during Chapter II - The Walls Have Ears:
The young prince was found guilty of poisoning Saskia, but he could consider himself lucky as he was merely imprisoned, and not torn to shreds by the mob.