Before anything else: I've seen that Wikipedia table before. What kind of crazy math did they do to arrive at 2.6 million Zoroastrians? That's about an order of magnitude too much. They must be including Yazidis or something.

Anyway, there are a few premises we need to pick apart here. First, the idea that there is anything remotely like single Middle Eastern culture is just not true, particularly not historically. At best, one can draw some very, very broad strokes to connect speakers of Afro-Asiatic languages (but hardly even that), but other groups such as the Indo-European Hittites and Persians were incredibly influential in the region as well.

Second, you are naturally including Christianity here. While Christianity has its root in Judaism, it was also heavily influenced by Greek thought (as was Islam, of course, but not quite to the same degree). The early Christian authors were all either Hellenized or outright Greek. The version of Christianity that came to be considered orthodox was also one where most or all ritual elements of Judaism were eliminated (circumcision, dietary restrictions, etc). This allowed it to grow popular in the Roman Empire, which is really the sine qua non factor for the spread of Christianity.

Third, Christianity and Islam span an impressive space indeed... but on the other hand, so did Indo-European religious traditions, once upon a time (and, of course, Buddhism and Hinduism are still widely practiced).

Fourth, obviously, entire books can and have be written about exactly why Christianity and Islam were succesful. But we can at least look at a few factors they have in common:

1. Proselytization and universalism. This is possibly the single most important one. Christianity and Islam both generally mandate that everyone ought to convert to Christianity or Islam respectively, and its adherents actively work to make this happen and to make sure converts practice it "correctly". That's not a common feature among religions.

2. Empire-building. I mentioned the Roman Empire before, and obviously, the establishment of the early Caliphates were absolutely key to Islam's survival and gradual entrenchment in West Asia and North Africa. Moreover, Islam wasn't just the religion of the elite, it was the justification for the state's authority. That wasn't unique, but combined with a proselytizing streak and the provision of social benefits on conversion it's not strange that conversions gradually happened.

3. Greek thought. I think this has some importance - Greek thinkers were very important to Islamic writers as well. What that provides is arguably tools of persuasion and resolution of apparent contradictions, and perhaps it even helps provide spiritual comfort by addressing the big questions of existence. It allows adherents and proselytizers to make stronger claims about the importance of conversion, since they will more readily be able to argue in favour of it. This idea certainly shouldn't be taken too far, though.

4. Ritually, relatively straightforward. Christianity and Islam do not necessitate costly sacrifices. Islam does have a large amount of ritual purity, but not as the primary focus of the religion. Christianity at its core requires you to say a creed, be baptized and take communion. Islam requires you to say the Shahada (There is no god but God, Muhammad is the messenger of God), though with many other strong recommendations as well.

Many other aspects of the religions could be considered, and all of these points have certainly been argued against at one point or another. But as you can see, the most basic features that appear to have made Christianity and Islam succesful weren't really particularly "middle eastern" (whatever that would mean in the ancient world) except maybe for the fact that Greater Syria, Asia Minor and North Africa were home to many major population centers and the breadbaskets of empires in antiquity.