Is the subject of The Iliad the wrath of Achilles?
As the previous answer notes, The Iliad contains much more than just the wrath of Achilles, including the stories of individual Greek warrior-kings--Agamemnon, Menelaus, Nestor, Odysseus, Diomedes, the two Ajaxes--and their Trojan counterparts, chiefly Hector, but including Paris and Agenor and other Trojan warriors. But the central element of the poem is Achilles' decision to withdraw from the battle and the consequences of that decision. A recent translation of The Iliad emphasizes the disastrous nature of Achilles' anger at Agamemnon:
Wrath, goddess, sing of Achilles Peleus's son's/calamitous wrath, which hit the Achaians with countless ills--many the valiant souls it saw off down to Hades. . . . (Peter Green trans., I:1-3)
As translator, Green focuses on the many Greek warriors whose deaths are directly related to Achilles' withdrawal from the fight because, when Achilles withdraws his and his Myrmidons support, that void is then filled by Hector and other Trojan warriors. During Achilles' absence, for example, Hector and the Trojans push the Greeks back to their last defensive position, threatening the Greeks' ships.
When we are immersed in the poem--which refers to numerous events outside the scope of The Iliad--we forget that we are reading about a two-month period (roughly) in a ten-year war that has consumed an entire generation of Greek and Trojan warriors. Within that ten-year period, the Greeks--because Troy itself is so well protected--have been raiding and pillaging all the smaller towns surrounding Troy, and Achilles' wrath is directly related to an attack on one of these towns in which he captures a young woman, Briseis, who becomes the cause of Achilles' anger when Agamemnon, in a stupid power play to show his ability to take something even from Achilles, takes Briseis as compensation for having to give up another captive woman, Chryseis.
The centrality of Achilles' wrath at Agamemnon and its resolution becomes clear in Book 19 when, after the death of his friend Patroclus, Achilles' wrath shifts from Agamemnon:
'Son of Atreus [Agamemnon], was it really the best thing for both of us,/ . . . should rage on in heart-rending strife because of a girl? . . . Fewer Achaians then would have bitten the boundless earth/at the enemy's hands. (Green, trans. 19:56-62)
Of course, Achilles is more interested in killing Patroclus' killer, Hector, than he is saving other Greek warriors, but the undeniable fact is that when Achilles rejoins the war--and especially after he kills Hector, the leading Trojan warrior--the Trojans' are living on expensively borrowed time as Achilles goes through Trojan warriors like a scythe through dry wheat.
In sum, then, it is correct to say that The Iliad is not only about the wrath of Achilles, but Achilles, his pride, his skills as a warrior, and his anger are at the center of the poem.
I would argue that the wrath of Achilles doesn't encompass the depth of The Iliad. To a modern reader, the Iliad is about how individual small actions lead to huge events and how no one person or event is unrelated to another. And this interpretation is driven by the weaknesses of each individual in the story. In that regard, Achilles' wrath is one element. So is Agamemnon's anger. So is Paris' dalliance. So is Hector's failure to grasp the greater war he is in, beyond his immediate battle. Each figure serves a purpose, and Odysseus becomes both a commentator with the wisdom of long years of war. It's the nature of the epics that they tell many stories, some captured in one night of storytelling and some captured over the length of the epic. That's entertainment, which is what they originally were. What makes them great entertainment is how a larger lesson is learned by the listener (or reader) as the epic progresses. That, one might say, is the subject of the Iliad.