Muslim armies at the time, mainly Ilghazis army were primarily made of Turkmen nomads. These nomads liked short campaigns and lucrative raids, however long sieges where one would sit in front of city or castle walls weren’t popular. These nomads would rather just plunder what was in the open, and go back to their horses and sheep. Another thing to note about them is they did not recognize the local emirs/beys as their rulers. These were wild men of the steppe. They avoided paying taxes and disobeyed laws. When things got tough, they would just move somewhere else without any regard for land ownership. Even the Turkish sultanates including Safavids and Ottomans had a hard time controlling the nomads. As a result, the nomads made for undisciplined armies. A Frankish serf or noble would face repercussions for deserting the army of the king, meanwhile the nomads would just move somewhere else.

Seljuk leaders were especially plagued by anarchy after death of Malik Shah. Seljuk central authority was non existent, and the various armies fielded by them would have very shaky chain of command. Among crusader armies you would have knights, and counts and the king, or an appointed commander above them. Meanwhile Seljuks armies a lot of the time would just have a bunch of lords that were not under a single commander and functioned as looser alliances. These commanders/lords would work with each other when it suited them, and simply desert when it didn’t.

I’d say what the author said is true for this time period. Two main Muslim states, Seljuks and Fatimids were collapsing at the time, and especially for the Seljuks the government authority was non existent. Without a legitimate state to pay and feed armies Muslims couldn’t maintain their armies. Though this changes with Zengids and later Ayyubids who built more centralized states that were as capable as any other state in the medieval times.