Well, they certainly had many nomadic tribes, but there were also city states like Mecca (which was an important hub of trade and worship, since Hajj was an activity before Islam) and Yethrib (now Medina). Poetry was still values post-Islam, as many of the greatest poets came from the Omiad and Abbasid Caliphates. Al-Mutanabbi, who is widely considered the greatest Arabic poet in history, was from the Abbasid era.

Though the pre-Islamic era had the writing of the Mu'allaqat ("the Hanging [poems]"), some of the most important poems in history, which were hung on the Kaaba (pre-Islamically) in reverence of them.

So yeah, poetry was relevant for a long long time in Arab society. Up until the previous century even. Hell, they are still often sung sometimes.