How does the Earth's eastward motion figure into the tracks proposed by Inmarsat data etc?
Not significantly. The aircraft flies in the air. The air moves over the earth and takes the plane with it. Of course wind is affected by the rotation of the earth, but there is little direct effect of Earth's rotation on the motion of the plane. The coriolis forces have a negligible effect on the aircraft's track.
The Inmarsat satellite used is geostationary, so it rotates as fast around the earth as the earth around its axis. The nett effect is zero.
The problem with this question is that there is a seriously wrong assumption behind: you are assuming that the airplane drifts along a course, like a curling stone after being launched, and is affected by all kind of environmental disturbances.
The thing is that the airplane has engines and control surfaces, in the case in question even an autopilot: if a certain course/track is selected, the plane will follow it, eventual wind will simply change the attitude at which the plane is flying (yaw for side component, pitch for front component), not the ground track. Unless you are in sidewinds/headwinds that exceed the top airspeed of the aircraft, but that was not likely the case.
The earth's rotation affects aircraft in much the same way as it affects you and I on the surface. From that perspective we are all being carried along at around 1000 MPH. Since the atmosphere is a very very very thin layer of gas above the surface, it pretty much rotates with the surface. You'll notice the oceans don't slosh across the continents every 24 hours too.
As Federico pointed out, following a constant magnetic heading from a fixed point on the surface will not be affected by the speed of rotation of the planet. Your navigational frame of reference is earth-centric not solar-centric (say).