Perhaps the “commandments” were something else? Could one be engaging in mere or rampant extrapolation to say that “Tis verse is a clear inference to the existence of the oral Torah.” And you yourself say that it is inferred. It could mean something else.
Was the Oral Torah passed from father to son and teacher to disciple without any possibility of human error? Was this transmission absolutely perfect in every way, form and fashion, so that no possibility of error exists today?
Why not write it down then and there (at least part of it in Moses’ time) so as to eliminate this possibility of error?
Keep in mind there are various classes of mitzvot (aka commandments) of the 613 listed here.
http://www.hebrew4christians.com/Articles/Taryag/taryag.html
All 613 are listed here.
http://www.jewfaq.org/613.htm
One of these are the “Chukkim” (aka statutes) which are given and have no reason as far as we can tell.
Let’s look at Deuteronomy 12:21
“If the place that the LORD your God will choose to put his name there is too far from you, then you may kill any of your herd or your flock, which the LORD has given you, as I have commanded you, and you may eat within your towns whenever you desire.”
There is no information given in the Written Torah as to the proper procedure for slaughtering kosher animals or even why it is supposed to be done.
If you study Oral Torah you’ll find out how to do the the slaughtering properly and correctly. It’s very detailed and requires quite a bit of training to be able to do it right.
Oral Torah also tells us how the words were spaced in the Written Torah as well as the cantillation and the vowelization of the words.
Articles here about the proofs of the Oral Torah.
http://www.aishdas.org/student/oral.htm
http://en.wikipedia.org/wiki/Oral_Torah
https://www.youtube.com/watch?v=vgmBLSfqX9I
It’s not that the Oral Torah was inferred from the Written but that the evidence of the Oral Torah can inferred by what is and isn’t written in the Written Torah. Moshe had questions that right when he questions, the 70 Elders who followed him had questions, and the rest of B’nai Yisael had their questions, too.
Moshe would go to God and He would explain it. Then he tell the 70, then the 70 would tell all of the men from the various tribes, then those men would tell it to their sons, so on and so forth.