The short answer is…Yes. According to the text in Genesis 5 through Genesis 10, every person living today is a descendant of Shem, Ham, or Japheth.
Reading Gen 5:32 through Gen 10:32 reveals that Noah only had three sons (i.e. Shem, Ham, and Japheth). Noah and they were the only males who entered the ark, survived the flood, and exited the ark. Right after the flood, God addressed only Noah and his three sons, but their names aren’t given until Gen 9:18-19.
Gen 5:32 (NASB)
Noah was five hundred years old, and Noah became the father of Shem, Ham, and Japheth.
After the flood:
Gen 9:1 (NASB)
And God blessed Noah and his sons and said to them, “Be fruitful and multiply, and fill the earth.
Gen 9:7-9 (NASB)
“As for you, be fruitful and multiply; [f]Populate the earth abundantly and multiply in it.”
8 Then God spoke to Noah and to his sons with him, saying, 9 “Now behold, I Myself do establish My covenant with you, and with your [g]descendants after you;
Gen 9:18-19 (NASB)
Now the sons of Noah who came out of the ark were Shem and Ham and Japheth; and Ham was the father of Canaan. 19 These three were the sons of Noah, and from these the whole earth was [i]populated.
Noah’s death is in Gen 9:28-29. However, Gen 10 then confirms he did not have any sons after the flood as it shows the three sons’ descendants. They’re grouped/shown with Japheth’s first, Ham’s next, and Shem’s last. That ends with “These are the sons of Shem, according to their families, according to their languages, by their lands, according to their nations. 32 These are the families of the sons of Noah, according to their genealogies, by their nations; and out of these the nations were separated on the earth after the flood.” (Gen 10:31-32 NASB)
In summary, since (1)-Noah had only those three sons, (2)-the only males who survived the flood were Noah and his three sons, (3)-only they were present after the flood when God told them to multiply, and (4)-“from these the whole earth was [i]populated.” (Gen 9:19 NASB), everyone today must be a descendant of Shem, Ham, or Japheth.