The Alshich (quoted as a commentary to the link you posted) provides an explanation, but you have to first read the verse before the penultimate one to understand it.
The verse before says
ויפרקנו מצרינו כי לעולם חסדו
This is commonly translated as "And He saved us from our enemies for His kindness is eternal." However, the Alshich seems to use the more literal translation for מצרינו , which would be "from our pain", and understands the verse as follows. When Yehoshua circumcised the Jewish people, that pain stood in place of our lives, and effectively stood as some sort of atonement, saving the Jewish people. Then he goes on to say the part that's relevant to our line: if there is no Jewish people, there is no world. Therefore, He saved us with our pain by circumcision, for "He renders His kindness to the world" = כי לעולם חסדו. (Note that he does not translate עולם in the phrase כי לעולם חסדו as "eternal", but rather literally, as "world". )
Now for our line (...נותן לחם לכל בשר), he says that after the circumcision, the Jews would not have had anything to eat until the Omer sacrifice would be brought, when they would be allowed to use the newly planted grain in the land (typically Jews can use old grain, but this was the first crop so they didn't have any). Therefore, Hashem miraculously gave them bread until that Passover (when they would be able to offer the Omer), which again saved the Jewish people, which saved the world as we explained with regard to the previous verse. Once again, this is כי לעולם חסדו "for He renders His kindness to the world".
I believe that according to the Alshich, you are right that it's chronological, since he ascribes our line to an event after the events of the previous one.