Strange Encounter on the Road

This did not happen to me, it was a story told to my father by my grandfather, who now told me. I am recounting it exactly as he told it:

This event took place in Egypt:

It was in the early 1930's on the desert road from Cairo to Alexandria in Egypt. My grandfather was traveling with a friend and just as they left Giza, the three pyramids were glistening under a full moon. The road was a single straight ribbon of asphalt, surrounded by the desert sand. The headlight added a faint glow to the desert road bathed in the moonlight. It was two to three hours before dawn.

As the pyramids disappeared to the left of the car, my grandfather noticed a person standing at the edge of the road, apparently hitchhiking. What puzzled my grandfather and his companion, was the fact that there was no disabled vehicle or crossroads at this spot. Where was that individual coming from in the middle of the vast desert? As the car slowed down, my grandfather noted that the individual was rather tall, and did not carry any luggage. As the car came to an almost complete stop, the two riders noticed in horror that the man's feet were hoofed like a goat, and they sped away in terror with this creature in hot pursuit. This thing continued to chase the car...even at 50 miles per hour. Only when the speedometer was over 80 miles per hour, did they notice in the rear view mirror, that the creature was fading back and had stopped running after them. Shaken and bewildered, they sped through the night until daybreak. To date, no one has explained this apparition.

I know it sounds very, very strange...but I can say for sure my grandfather was a very truthful, sane, and down to earth man...He was also traveling with another man when seeing this....

So what do you think that was? I can't find any good way to explain it...