I think they're asking if not using npm or similar, what is the process for updating your local copy of a file/package.

Which would be, go to where project is hosted, find out what version you're looking for, click until you find actual source, copy text or download file, move file from downloads to your repo, or paste in to a new file in your repo.

Make works well for me...

  TMPDIR=$(BASEDIR)/tmp

  THEME=$(BASEDIR)/theme
  THEME_CSS=$(THEME)/css
  THEME_FONT=$(THEME)/fonts
  THEME_JS=$(THEME)/js

  VER_BOOTSTRAP=3.3.6
  VER_FONTAWESOME=4.5.0
  VER_JQUERY=2.2.1

  updatedeps: $(TMPDIR) bootstrap fontawesome jquery

  bootstrap:
	curl -L -o $(TMPDIR)/bs.zip https://github.com/twbs/bootstrap/releases/download/v$(VER_BOOTSTRAP)/bootstrap-$(VER_BOOTSTRAP)-dist.zip
	unzip -j $(TMPDIR)/bs.zip bootstrap-*/js/bootstrap.min.js -d $(THEME_JS)
	unzip -j $(TMPDIR)/bs.zip bootstrap-*/css/bootstrap.min.css -d $(THEME_CSS)

  fontawesome:
	curl -L -o $(TMPDIR)/fa.zip https://fortawesome.github.io/Font-Awesome/assets/font-awesome-$(VER_FONTAWESOME).zip
	unzip -j $(TMPDIR)/fa.zip font-awesome-*/css/*.min.css -d $(THEME_CSS)
	unzip -j $(TMPDIR)/fa.zip font-awesome-*/fonts/*webfont* -d $(THEME_FONT)

  jquery:
	curl -L -o $(THEME_JS)/jquery.min.js http://code.jquery.com/jquery-$(VER_JQUERY).min.js

This is actually a shell script in disguise. If this is all you do with make, I suggest you make this into a shell script:

  <Makefile sed -E 's/.*:$//; s/\(|\)//g; s/^updatedeps:.*/mkdir -p $TMPDIR/' > update-deps.sh
  BASEDIR=$PWD sh ./update-deps.sh

Make is for generating output from interdependent input. It can be used for minifying your JS, or compiling your CoffeeScript in to js, or your sass (but that is handled mostly by respective compilers, tho I prefer running the compiler myself) (also, I don't use coffeescript or sass, so IDK if I'm mistaken).

No my point is redundant. How would one manage upgrading dependencies without using a package manager? Why would anyone advocate against a package manager, no matter what the size of the dependency is?