On taking out the Torah we say, "and the word of Gcd will come forth from Jerusalem" (paraphrased). What does that mean? It does not say "the word came forth from Sinai". Does it mean that the Jews will be a light unto the nations by teaching the law in Jerusalem?
דבר ה' הוא הנבואה, ותורה היא תורת משה
Firstly he teaches defines the words:
- Dvar Hashem refers specifically to prophecy.
- Torah refers to the Torah, as we know it.
Then he explains the verse in detail:
תצא תורה, לכל העולם כמ''ש כי יפלא ממך דבר למשפט וכו' וקמת ועלית וכו', וזה היה רק בציון, ודבר ה', הוא דבר הנבואה (תצא) מירושלם, ששם היו הנביאים מתאספים, שואבים רוח ה' בכל העיר, כי הנביאים לא ישבו בלשכת הגזית. וכל זה דברי העמים זה לזה.
Torah comes forth from Tzion (the Holy Temple) - since that is where the Highest Sanhedrin sat and decided all queries that arose.
Dvar Hashem - prophecy - comes forth from the entire city of Jerusalem, where the prophets tended to gather, as the holiness of the city was conducive to prophecy.
I think you'd have to ask Isaiah, since it's a quote from Isaiah 2:3.
If you read the rest of the chapter, it's a vision of how the world to come will be like. It seems to center on other nations acknowledging Hashem and His word, laws, etc.
Since earlier in the chapter, it says that the Lord's house will be established in Jerusalem, it stands to reason that this is where the word will come from.
Hope this helps.
Shemaisrael.co.il writes on this subject:
One of the most moving descriptions of the universal pilgrimage to the Temple is found in the following prophecy which describes the Temple as an educational center for all peoples: “It will happen in the end of days: The mountain of the Temple of Hashem will be firmly established as the head of the mountains, and it will be exalted above the hills, and all the nations will stream to it. Many peoples will go and say, ‘Come, let us go up to the Mountain of Hashem, to the Temple of the God of Jacob, and He will teach us of His ways and we will walk in His paths.’ For from Zion will go forth Torah, and the word of Hashem from Jerusalem.” (Isaiah 2:2,3)
In his commentary on a related verse, Radak explains that when the peoples make the pilgrimage to the Temple, they will seek to study and fulfill the Torah’s universal moral code – The Seven Mitzvos of the Children of Noah (Commentary on Isaiah 42.6).
So rather as you say we will be teaching the law in Jerusalem – very soon we hope.