No he did not. The second half of the quote is ascribed to Friedrich Engels, and was written in the Marx People's Paper as the image correctly mentions. Evidence of it being Engels' and not Marx can be seen here at page 137: https://www.jstor.org/stable/2709420
In the link above a translation can be seen where they translate "weltsturm" into "Holocaust".
This is the original quote:
"Alle anderen kleinen Stämme und Völker haben zunächst die Mission, im revolutionären Weltsturm unterzugehen."
Just copy-paste the above in google (without the brackets) and you'll see a plethora of different websites containing it exactly like that and no other way.
Welt means world and sturm means storm. World-storm is the exact translation. Holocaust comes from the greek words holos en kaustos (respectively "whole" en "burnt" or wholly burnt) and is nowadays commonly known as the word that is used to denominate the the genocide of jews in the second world war.