Ba'al ha'Turim: It says so in one other place (Shemos 13:19) - Yosef made his brothers swear [to take his bones to Eretz Yisrael]. The Mechilta expounds that he obligated them to make their children swear. Also here, Sha'ul made people swear to impose the oath on others who were not there. Therefore, Yonason was liable.

Radak: Even though they are fatigued and hungry, they did not transgress the Shevu'ah.

Malbim: He proved that the decree was even for tasting. The nation is fatigued and cannot chase the enemy. If it were only lest they delay for a meal, it would be better to eat, and get renewed strength to chase! Rather, he decreed a fast to Hashem, who gives to strength to the weary.