Excellent question about this frequent Hebrew phrase, עַל־כֵּ֠ן "al-ken" (literally, "upon thus") which is almost universally translated, "therefore". I will avoid a commentary on the OP's reference (whose author is unstated!!) and its frequent leaps of logic and misquotes and concentrate on the OP's question about the claims surrounding "al-ken" indicating the initiation of an institution.
עַל־כֵּ֠ן "al-ken"
The OP's reference helpfully provides a list of the occurrences of עַל־כֵּ֠ן "al-ken" which shows how it is used. Most of these are simply a list why something is known by some name (eg, Gen 10:8, 11:8, 16:13, 19:31, 25:29, 26:32, 31:47, 33;16, 50:10, etc). Unfortunately for the OP's reference, it does not universally indicate the start or initiation of something. It simply means, "as a consequence of", or, "therefore".
For example, we have Eze 7:20; 22:4; 31:5, etc. Further, the author did not list a number of instances such as Isa 24:6, 30:16, 50:7, etc.
However, even if we accept the author's premise based on a tangential comment of Gill, we still cannot arrive at the author's contention in Ex 16. Let me be more specific. Ex 16:29 says this:
Understand that the LORD has given you the Sabbath; therefore on
the sixth day He will give you bread for two days. On the seventh day,
everyone must stay where he is; no one may leave his place.
Note that this is precisely the reverse of the OP's reference author's contention - the Sabbath was not initiated in Exodus 16, it was the double manna on Friday that was initiated; that is, the double manna was initiated as a result of the already existing Sabbath!
The same is true in Ex 20:11 - the Sabbath was hallowed at creation (as Gen 2:1-3 makes clear) and Ex 20:11 simply repeats what Gen 2:1-3 records; that is, the Sabbath was created/initiated on the seventh day of creation week and hallowed, and Ex 20:11 simply repeats this information.
Lev 17:11 is another example of the exactly the same thing - Israel was commended not to eat blood as a reminder of the command given in Gen 9:4, 5. This shows that עַל־כֵּ֠ן "al-ken" cannot be used as marker of the initiation of something new.
Deut 5:15 is another example of the same thing. Deuteronomy was written about 40 years after Exodus but still lists the reason for keeping the Sabbath as Israel's release from slavery in Egypt which was not initiated when Deuteronomy was written but 40 years earlier! The author even admits this but still presses the point about the Sabbath despite the evidence to the contrary.
This is consistent with all the rest of the 10 commandments - all existed before Ex 20 as shown in the appendix below.
APPENDIX - Ten Commandments before Sinai
The following (far from exhaustive) list shows that people knew of the ten commandments well before the formal giving at Mt Sinai. Indeed, we have the very general comment –
- Gen 26:5, because Abraham listened to My voice and kept My charge, My commandments, My statutes, and My laws.
Commandment #1 – Worship only YHWH:
- Gen 22:5, 24:26, 48, 52 all describe worship of the true God of heaven, YHWH.
- Gen 35:1-4 – Jacob instructs his whole household to eliminate all foreign gods
Commandment #2 – Idolatry prohibited
- Gen 31:32-35 – Jacob clearly understood that idolatry was forbidden.
- Gen 35:1-4 – Jacob instructs his whole household to eliminate all foreign gods
Commandment #3 –Cursing and taking the name of the LORD in vain prohibited
- Job 1:5 – When these celebrations ended—sometimes after several days—Job would purify his children. He would get up early in the morning and offer a burnt offering for each of them. For Job said to himself, “Perhaps my children have sinned and have cursed God in their hearts.” This was Job’s regular practice.
Commandment #4 – Sabbath worship
- Gen 2:1-3 – Thus the heavens and the earth were completed in all their vast array. And by the seventh day God had finished the work He had been doing; so on that day He rested from all His work. Then God blessed the seventh day and sanctified it, because on that day He rested from all the work of creation that He had accomplished.
- Ex 5:5 - And Pharaoh said, “Behold, the people of the land are now many, and you make them rest [שָׁבַת shabath] from their burdens!”
- Ex 16 also records the incident with manna and that collecting manna on the seventh-day Sabbath was forbidden
Commandment #5 – Respect for parents, elders and authority
- Gen 28:6, 7 tells of the story of Jacob following his mother’s advice. Respect for parents is built into the very fabric of the patriarchal stories in Genesis.
Commandment #6 – Sanctity of Human life
- Gen 4:8-12, 15 records Cain’s punishment for the sin of murder
- Gen 4:23, 24 – Lamech realises that he has murdered someone and will suffer consequences
- Gen 9:5, 6 records that murder was prohibited under the ancient Noahide covenant
Commandment #7 – Adultery prohibited
- Gen 12:10-20, 20:1-17, 26:6-11 all record “adultery narratives” in which the patriarch is (correctly) chided for almost tricking a pagan king into committing adultery
- Gen 19 records the appalling events involving attempted pack-rape of the two angels
- Gen 39:7-9 – Joseph calls Potiphar’s wife proposal “a great evil and sin against God”.
- Gen 49:4 – Reuben is scalded for his sin of incest
- Gen 34 – the story of Dinah records a heinous incident involving her defilement (plus murder and lying)
Commandment #8 – Stealing prohibited and respect for property
- Gen 30:33 – Laban and Jacob discuss the problem of stealing of wages and property
- Gen 31:32-35 – Laban is angry about the sin of stealing the household gods
- Gen 44:9 – Joseph’s brother accused of stealing his divination cup.
Commandment #9 – Lying prohibited; insistence of honesty and integrity
- Gen 4 – the story of Cain being punished, among other things for not being honest with Abel and God in his statements
- Gen 12:10-20, 20:1-17, 26:6-11 all record “adultery narratives” in which the patriarch is (correctly) chided for lying to a pagan king about their marital status
- In the story of Jacob, he is pejoratively called Jacob = “deceiver”, Gen 27:36.
- Gen 37:31-33 – Jacob rebuked for lying and deception
Commandment #10 – Coveting prohibited
- Gen 3:6 – the woman is tricked by the serpent using the sin of covetousness
- Job 31:9, 10 – Job says he is innocent of coveting his neighbour’s wife.
Other Laws
Even the prohibition against eating blood is listed among the requirements in the Noahide covenant, Gen 9:4, 5.
