Have you listened to the history of Byzantium podcast, OP? I recommend that you do if you're interested in this time-period.
Basically the size of the Byzantine empire at the end of the war against the sassanids occludes what shitty position they actually were in. A few key points that people commonly misunderstand explain why the arabs could snatch so much area in just a half century:
>Imperial cohesion
Many people look at historical maps like the one in the OP and assume that the countries or empires that they're looking at are homogenous and unitary states when they were in effect loose federations of different peoples with different economic, cultural, and geographic dispositions. One of the key reasons Constantine pushed christianity as hard as he did was that it was basically the only unifying force he saw that the entire empire could have in common.
Many people see the dissolution of the Western empire in terms of a foreign conquest by migrating barbarian tribes, which the state, as well as the people, struggled against up until the very end. In reality many regions welcomed the invaders because the increasingly centralised Roman state kept levying higher and higher taxes while at the same time failing to uphold their obligations toward the periphery of the empire. Not only were they failing to defend the borders in a military sense, they were also neglecting local administration; being a local town leader was basically a dead-end career by the 5th century. In effect, the social contract was broken and the invaders offered better deals.
The same thing happened in the East, especially after the fall of the West. The economic burden of the empire increasingly fell on the cities of the levant and Egypt. Greece and Anatolia were basically flyover states at this point, and while Constantinople was the largest city in the Western hemisphere, most of its population was dependent on the grain and wine dole coming in from Alexandria.
This bred discontent in the populations actually forced to pay the brunt of imperial taxes, it didn't help that they were also the most heavily populated areas outside Constantinople as well and therefore had to supply most of the recruits for the army and navy.
Come the last Sassanian war, the East Roman social contract was broken. The levant and parts of Egypt came under sassanian rule for a whole generation. Heraclius (the emperor at the time) was obliged to have the church melt down their precious metal decorations in order to fund one last army which just barely managed to kick out the sassanids after twenty years of continous campaigning.
A consequence of this is that an entire generation had grown up in the levant used to a different government than the roman state, and didn't really take kindly to when the romans came Rolling back in and started to demand the same taxes as they had received half a century earlier.
>Arabs not assimilating conquered populations
This played an immense role when the Arabs came ten years later. After the Yarmouk, most towns in the levant basically opened their gates to them. The opinion at the time varied from "they're just desert raiders and the roman army will soon be here and kick them out again" to "fuck the romans".
The arab state (if it can even be called that) was much more decentralized than the roman counterpart, and they barely interfered in the day to day business of conquered areas. They even kept to themselves and housed their soldiers and imported populations in newly created garrison towns outside the main settlements, so the conquered peoples didn't even see their conquerors.
In the beginning the arabs didn't even force conversions or apply jizya, they. instead allowed most people to keep being christians. There are moderns scholars who argue that Islam at this point wasn't even formed as a coherent religion, and rather just a branch of Judeo-Christianity.
This initial reluctance to interfere greatly increased local acceptance of the new regime and allowed the arab armies to focus on keeping the rape train going rather than put down brewing revolts.