Will righteous non-jews also partake in Techiyat Hameisim, resurrection? Will they be brought back to life in the time of the Mashiach?
Will Noach? Abraham? Malki-Tzedek? Shem? etc.
The short answer is yes, they will be resurrected. See from Sukkah 52b:
The Gemara continues homiletically interpreting verses that relate to the end of days. It is stated: “And this shall be peace: When the Assyrian shall come into our land, and when he shall tread in our palaces, then shall we raise against him seven shepherds, and eight princes among men” (Micah 5:4). The Gemara asks: Who are these seven shepherds? The Gemara explains: David is in the middle; Adam, Seth, and Methuselah are to his right; Abraham, Jacob, and Moses are to his left. And who are the eight princes among men? They are Yishai, Saul, Samuel, Amos, Zephania, Zedekiah, Messiah, and Elijah.
Please note that Adam, Seth, Methuselah, Abraham and Jacob were all prior to the giving of the Torah at Sinai. They are not Jewish. Their status is that of non-Jew.
It should be pointed out in the context of current world affairs (פשר) that there is a distinct possibility this page of Talmud is speaking about the very near future.
I do not believe there are clear sources indicating that non-Jews will be resurrected (but see this other answer and comments below)
MyJewishLearning indeed writes
It is not entirely clear whether only Jews, or all people, are expected to be resurrected at this time.
and R Naftali Silberberg at chabad.org writes only about Jews
Every Jewish soul that ever lived will be resurrected.
(see also here from the same author)
There is a well-known Rambam (MT Hilchot Tshuva 3:5) that
the righteous among the nations of the world have a share in the World to Come
but the World to Come can refer to the spiritual after-life, beyond the era of resurrection.