Everybody seems to be missing the fact that he's not talking about building a big software project. He's talking about scripting a simple workflow around a few files. Make is probably better than anything else for this, because under these circumstances it's so simple it's hard to get it wrong.
Something like Rake is obviously better when you need to really program your builds.
I depend on make for recording a workflow history of my projects. There's no point in creating an alias in my ~/.bashrc for an arcane command I'm only going to use once or twice a year to transform, sync or configure a group of files. When I check a project out of version control, it's nice to have a Makefile there to remind me how I accomplished something.
Make allows you to consistently specify actions in a universal way. Typing 'make edit' will open the main file in vim for me in any project. Typing 'make update' will check for available updates on any platform using the appropriate package manager, and 'make upgrade' will download and install them. Typing 'make sync' will transfer my project files to the specified $SERVER as the specified $USER with the appropriate protocol. Typing 'make install' will copy an updated configuration file and restart all of the daemons necessary for it to work. It's a great timesaver. Even when I need to write shell scripts for something too elaborate for make, I tend to create a target that runs the script, instead of trying to remember its name and all of the options.
I wanted to say exactly this. I wouldn't choose Make to build a software project these days (probably), but I use it all the time for exactly what the author describes: recording/managing a data processing workflow. For stats/ML exploratory work, it's invaluable, because everything you do is recorded in various targets. It makes my one-off scripts not quite so one-off, so when I revisit the code six months later, I can quickly figure out what I was doing. It also means less typing, because every command is just `make foo`, and that delegates out to R/Ruby/Python scripts, shell pipelines, or whatever I need. I'm delighted that someone else is (ab)using make the same way!
Something like Rake is obviously better when you need to really program your builds.