Due to problems with my image server, the maps will be down
I can't do much better than refer readers to Chester, who has carefully plotted all the known incidents of Operation Matador on a map, together with a chronology of when each happened. The enemy delivered mortar fire as the assault began on Sunday and delivered a night-time combined arms counterattack on Monday and made various attempts to escape by boat or vehicle on Tuesday. The list of incidents and chronology belie the assertion that the enemy was gone before the Marines arrived. Chester's map is reproduced below.
One gets the sense that the fluid part of the battle ended on Tuesday morning and that whatever enemy survived the initial confused hours have now hunkered down to sell their lives dearly. The use of AT mines, armor piercing ammunition, mortars plus the provision of enemy troops with body armor suggest the presence of above-average combatants. Chester concludes:
Analysis: The terrorists are dug in and fighting, or at this point, fought, in Ubaydi and Rammanah. The number of attacks on Hwy 12 leading to Al Q'aim suggests that terrorists fleeing to Syria are attacking and being attacked by an increased Marine presence on the Hwy. Those that escape this force must then make it past Camp Gannon to withdraw to Syria. All of these attacks are on the south side of the river, which may not be what was expected.
Fortunately, the Keyhole company has added a new dataset to their mapbase which allows for greater resolution of some of the key areas. If we focus on Rammanah, which is in the bight of the river above, we get the image below. You can clearly see the road as it departs from the marked GIS blue road line and goes into the village, which is apparently built on a low scarp overlooking the fields. The houses are white dots. One possible reason the Euphrates was bridged south was because the enemy probably anticipated an attack from the north, along the existing road. Note also that if Chester's plot is correct, the fierce fight in Ubaydi (approximately where the blue line forks) represents a defense of the crossroads and the northern road approach into the town. Visually at least it is hard to see how resistance can be prolonged very long in a place like this.
There are only sparse clusters of houses between Rammanah and Qaim/Qusabayah and that may explain the dumb-bell shape of the pattern of engagements, although the plotted incidents on Chester's map may not be precisely located. The second image is of the actual border town of Qaim/Qusabayah. It is quite an extensive, nearly urban place and it is easy to understand why insurgents should flee toward the border. Even if they could not actually cross into Syria, there was probably some expectation of being able to hide in the bigger town compared to fighting it out in a farming village like Rammanah above. Clearing the hundreds or thousands of houses in the area of suspects will take time and soak up the efforts of the Marines.