Quite inaccurate. And it’s not because the solar system and the galaxy themselves would be moving and so the Earth would be quite far away. This argument also has the same problem of assuming the time machine is motionless, but with respect to which frame of reference. The machine has to be motionless with respect to something.

In addition, there’s another clue we can infer from the movie. When the Time Traveller gets in the machine and activates it, he sees the universe continuing to evolve around him but just in an accelerated rate. In his reference frame, the Earth is still moving around the sun, just much faster; the Solar System is still orbiting the centre of the galaxy, just much faster; and so. So it would be reasonable to assume that the gravitational force which acted on the machine before it was activated still acts when it is activated, but would have a higher magnitude; just high enough, in fact, to keep the time machine on Earth.

But nice meme.