Looks like you can just download the zip for "Snow Leopard and Above 64bit", unzip the file once it's finished downloading (by double clicking it or using the commandline tool unzip), and then you have the binaries.
Then you just have to decide where to put the binaries. Since you don't want an admin password, it's probably best to keep them in your home directory. Thus I recommend doing the following in your terminal:
mkdir -p ~/.local/bin
curl -L 'http://www.ffmpegmac.net/resources/SnowLeopard_Lion_Mountain_Lion_Mavericks_Yosemite_El-Captain_25.02.2016.zip' | tar -xf-
mv ffmpeg ffprobe ffserver ~/.local/bin
echo 'export PATH=$PATH:~/.local/bin' >> ~/.bash_profile
The above script will make a directory for the new binaries, then download the ffmpeg zip to your Downloads directory, then unzip it and move the binaries to that newly created binary directory, and then finally it adds a line to your bash environment so that your terminal correctly sources the binaries.