The Mongol Army was nothing special. Genghis Khan deserves credit for forging a united discipline army with good organization, but at its core it was composed of light cavalry with a core of heavy shock cavalry which was no match for a properly led Army of a sedentary state. When the Mongols met well led Armies, they got their asses handed to them. They were good at reducing isolated Earthen Walled Settlements, but were unable to take cities and fortifications with Stone Walls. They also sucked at logistics and several Mongol Battlegroups actually starved to death invading Hungary.
Genghis was also lucky to come at a time when the Northern Chinese, Qara Khitai, Khwarezmian Shahdom, et al were led by morons who let themselves be destroyed in detail.
Also the notion that Khwarezmian Shahdom sucks because it doesn't have decimal organization is nonsense. Also it had a postal system of messengers, pigeons, etc which had existed as far back as the First Dynasty of Egypt in recordings, and thus that is laughable. How do you think the Shahdom and all its contemporaries communicated internally and externally?
Under Jalal, who doesn't have his main power centers gutted, and can bring more troops to bear, he can definitely make a play for the Mediterranean and Transcaucasia. I give it even odds.
As for the Almohads, yes they got trashed at Las Navas de Tolosa, but it took a few more decades before they lost Cordoba and a few more before they collapsed. Plenty of time for Jalal or a successor if he is so inclined to send help, either in person or depending on the situation, in concert with the Ayyubids/Rum/Mamluks to check the advance of the Reconquista and stabilize the situation to status quo pre-Las Navas de Tolosa at the least.
And if Jalal takes the Abbasid Caliphate, he can simply absorb the Office himself, just have the Caliph adopt him as a son and heir prior to his 'retirement.'
Of course, I am also open to the ideal he may prioritize taking India and maybe taking the Qara Khitai instead.
There is much possibility for him to expand depending on his how priorities evolve upon taking power.
That stance ignores the Mongols' other strengths, particularly their versatility in manipulating the strengths of conquered peoples to augment & cover the weaknesses of their forces. They obviously could forcefully take strong fortresses (as places from Baghdad to Alamut & the other Hashashin forts to Xiangyang can attest to) and, if not technically proficient themselves, knew how to wield people who were. In Khwarazm's case they used captured Chinese technology and engineers to great effect - deploying gunpowder to crack open the citadel of Bukhara, for example - and later ironically using counterweight trebuchets from the Islamic Middle East against the Song at Xiangyang. We know they can beat competently led sedentary armies in the field as well, since they did just that all the time - whether Jalal himself at Indus, Henry the Pious and his Poles & crusaders at Legnica, or Bela IV and his Hungarians at Mohi (in that case, Bela survived to recover and rebuild Hungary to better withstand a future Mongol invasion, including storing provisions in such a way to starve the Mongols on their second attack in the reign of his grandson Ladislaus).
From the Khwarazmians being blindsided by Genghis' movement through the Kyzyl-Kum desert and only responding sluggishly to Mongol attacks, I think it's pretty safe to suggest that Mongol organization and communications exceeded whatever the Khwarazmians had. I'm also not sure what you're getting at by repeatedly raising the Mongols' enemies being led poorly and/or defeated in detail. Yeah that was true in many cases (and not in others, as I mentioned above), but does exploiting your enemies' weaknesses somehow detract from the glory and impact of victory? That's like suggesting the Rashidun Caliphate attacking the ERE and Sassanids after they had beaten each other (and themselves, what with Heraclius' revolt against Phocas and the Persian civil war immediately following their defeat) senseless for nearly 30 years somehow makes the early Muslim conquests less impressive or respectable. I don't believe we can fault the Mongols for not chivalrously giving their enemies a fair fight or using opportunities those enemies created through their own mistakes.
Anyway, since this thread is about 'what if Genghis dies and so there were no Mongol conquests' and not the Mongols themselves...back on topic, were I the Almohad Caliph I would definitely not count on the Islamic powers of the eastern Mediterranean & beyond for help. If Jalal and the Khwarazmians look as though they're about to overrun the Levant, a Seljuk-Egyptian alliance to constrain them becomes exceedingly likely - in fact that's literally what happened IRL leading up to Jalal's final defeat at Yassicemen, and it occurred even though he seemed less threatening than he did in a no-Mongol scenario. If it looks like one of the other two has the upper hand, I expect the Khwarazmians and whichever of the other three isn't on top at that moment to ally instead.
In all three Muslim powers' cases the Almohads' problems are a very distant concern compared to their immediate interests (fighting the crusaders/Byzantines and competing with each other) much closer to home. I'd imagine any appeal for help from al-Andalus and the Maghreb will likely go down about as well as Boabdil's call in 1492, and much for the same reason: at that time the Mamluks basically told the Granadines 'too bad, sorry for your impending loss' because after all, they were busy trying to fend off their fellow Muslims, the Ottomans. Religious solidarity (especially in such far-off lands) tends to take a back seat to rivalries and competing interests in cases like these, much as the English wouldn't help Louis IX of France out in his ill-fated crusades just a few decades down the road because the French had been gobbling up their continental domains.
The Khwarazmians moving into India is an interesting possibility. If Jalal does that instead of striking west, he'd be following in the successful footsteps of the Anushtigins' Ghaznavid and Ghurid predecessors. It would put him in conflict with the Muslim Delhi Sultanate, but I don't see that stopping an ambitious and competent Khwarazmian ruler. IIRC Jalal's father, Muhammad II, actually did already attack the Indian Mamluks and wrest their portion of Afghanistan away from them a few years before the historical Mongol invasion anyway, so there's definitely precedent for that to happen if he so chooses.
