Can you explain why the gentiles do not have to keep the Shabbat? The way I read the Tanach, G-d commands all people to observe the day. So therefore I think it is a falacy for gentiles to not observe Shabbat.

The command is clearly to the Jewish People alone because it was only they who were saved by G-d from Egyptian bondage. G-d's creation of the world in six days is only one of the two reasons given in the Torah for Shabbat, the other is the Exodus of the People of Israel. Neither reason stands on it own. In fact it is the freedom of the nation of Israel from the yoke of other nations that attests to G-d's freedom from the laws of nature that were created in six days.