It's not a joke. It was quite a controversy, when Muntazer al-Zaidi thew his.
In Arab culture it's seems as an insult to show someone the soles of your shoes, throwing or hitting them with your shoes is even worse.
and
Incidentally shoes are much more symbolic in the middle east, not least of wealth and status, where it's common for poorer people to be unshod.
Anyway, it's seems fairly clear that the statue depicts Nouri al-Maliki. I'm not an expert but I'll try and roughly sketch what this may probably be about. The comic implies he was hated and didn't have popular support. Not unexpectedly since he was the leader of Iraq chosen by the U.S. and was torn between his nations best interests and those of it's occupiers. When he finally sided with his compatriots during the negotations over things like a new Status of Forces Agreement, and renegotiating contracts for Iraqi oil (many of which contracts passed during the upheaval of toppling Hussein, when the Iraqi government was effectively a US puppet regime, and Iraqis had no clout whatsoever in negotiations), and issues such as holding American troops responsible for crimes committed during the invasion of Iraq. They probably hoped Al-Maliki would turn into a sort of kinder gentler more manageable tyrant like Hussein, keeping his people down while foreigners could go about doing their business safely. The majority of Iraqis are Shia like Maliki, while Hussein was was from an enclave of the Sunni minority, and of course the country can't really be run democratically because it would naturally align with mainly Shia Iran and threaten their Saudi Neighbor to the south, who have a large Shia population right in the heart of the richest oil producing region, not to mention restive Kurds in the North.
Things came to a head and US signalled they wanted Maliki out, for not towing their line enough. There is some indications some of the religious tensions in the region were partly stoked to topple him (reduce the influence of his Dawa party I suppose) from power. Suicide bombings and such. You might recall the US basically disbanded the Iraqi army creating a huge unemployment problem and resulting in a great deal of restiveness and disaffection in the Iraqi population generally. Baathism was effectively proscribed among other popular political movements like those of Al-Sadr. The US were more interested in subverting oil workers in Basra attempts to unionize by simply killing them and destroying the Mahdi army defending them. This wasn't long after the systematic torture of prisoners in Abu Ghraib was revealed (the full extent of which, the grisliest details, like raping children in front of parents, murder and probably much worse, still hasn't seen the light of day). The real villians atop the chain of command were protected while peons like Lynndie England were scapegoated for following orders and doing their regular jobs. Some old same old. Anyway many former Baathists and other prisoners of war were eventually released from American custody in Iraq. Not coincidentally this is right around the time ISIS seemingly appeared out of nowhere. They took over major parts of northern Iraq, and threatened the Maliki government (after it lost disastrously trying to fight them), and the political situation created finally forced him from power. Of course the Americans have major bases and complete control of the air, so you can draw some easy conclusions. Anyway, after proving unable to handle Isis, and embarassing military defeats, Maliki was pressured into resigning. Conveniently after Malikis political ouster, Isis then started incursions into Syria, under the guise of spreading the 'Arab spring'. The original Arab Springs in Tunisia and Bahrain (and maybe Egypt) seemed popular, democratic and pacifist, quite different from the violent crackdowns in response. Violence gradually led to the ouster of Kaddafi and Maliki and appeared to be spontaneous threatening Bashar Al-Assads regime. Anyway, the gist I think is that Iraq is now fractured, politically, between all sorts of groups. Inner divisions among tribes, religious divisions (probably exaggerated for political ends), external influences from the U.S., Isreal, Jordan, Saudi, Iran, Turkey and Syria and probably more. All of that is on top of massive environmental problems, economic recovery problems, and the challenge of reconstructing within a culture of corruption and crime after years of Sanctions and destroyed infrastructure. Maybe in effect the country is now run by a whole bunch of small warlords, little Maliki clones. The shoe doesn't know who it needs to be thrown, there's too many targets.