Even under the Old Covenant these Gentiles had to keep the Sabbath day:
(Exodus 12:49) "One law shall be to him who is home-born, and to the foreigner who sojourns among you."
(Exodus 20:10) "But the seventh day is the Sabbath of the LORD your God; in it you shall not do any work, you, nor your son, nor your daughter, your manservant, nor your maidservant, nor your cattle, nor your foreigner who is within your gates:
(Exodus 23:12) "Six days you shall do your work, and on the seventh day you shall rest; that your ox and your ass may rest, and the son of your handmaid, and the foreigner, may be refreshed."
(Leviticus 24:22) "You shall have one manner of law, as well as for the foreigner, as for one of your own country: for I am the Lord your God."
(Deuteronomy 5:14) "but the seventh day is the Sabbath of the Lord your God: in it you shall not do any work, you ... nor your foreigner who is within your gates; ..."
(Isaiah 56:6-7) "Also the sons of the foreigner, who join themselves to the LORD, to serve him, and to love the name of the LORD, to be his servants, every one who keeps the Sabbath from polluting it, and takes hold of my covenant;
7 Even them will I bring to my holy mountain, and make them joyful in my house of prayer: their burnt offerings and their sacrifices shall be accepted upon my altar; for my house shall be called an house of prayer for all people."
The word foreigner in all these scriptures refer to someone who was not an Israelite.
Now the law applies (at least in a spiritual sense) to Gentiles as well as Jews, because "the Gentiles have been made partakers of their spiritual things," (Romans 15:27), and "the law is spiritual," (Romans 7:14).