Assuming I know some linear algebra, do I also need to know about the “traditional” machine learning algorithms before taking this course?
I’d say, just give it a go. In lesson 1 @Jeremy introduces deep learning very hand-on without much math formalism. You’ll train your first DL model with seven lines of code. The following lessons explain why and how it works.
If you find you need a primer there is Andrew Ng’s Machine Learning course on Coursera. There are numerous other links littered around this forum and the web.
Just give it a go and fill in the gaps as needed.
I would say the main thing you need is some bash and python knowledge. I knew little about either of those and even less about machine learning. It is a bit of a fire hose getting up to speed on all three. I feel like this is sort of the “wild west” days of ML and not knowing the “traditional” wisdom is probably a good thing! 
I did take Andrew Ng’s course on Coursera at the same time which was helpful for me to understand the maths behind it, but I don’t think you really need that to understand Jeremy and Rachel’s content.
And like @iNLyze said, “Give it a go.”