This is certainly an interesting and theoretically promising method, that, if it works, should make it fairly easy to develop specific personalized "vaccines" for each person's cancer.
For background, dendritic cells are a type of antigen-presenting cells, which means their job is to pick up proteins, break them up into small pieces (antigens), and then show those pieces to T-cells, whereupon the T-cells can either say "looks like a self antigen, everything's fine" or say "that looks like a foreign antigen, raise the alarm!" and then initiate a specific immune response against that antigen.
The basic concept here is that if you have a specific protein that you want to raise an immune response against, you can do so by tricking dendritic cells into producing copies of that protein, which will then get presented along with all the other antigens for inspection by T-cells. You can pull off this trick by feeding RNA that encodes the target protein to the dendritic cells, and as a bonus, the fact that there's free RNA floating around triggers anti-viral defenses, which causes the T-cells to be extra suspicious of the antigens they're inspecting (i.e. it lowers their threshold for raising an immune response). But injecting RNA directly into your spleen isn't exactly practical, so instead they found that attaching the negatively charged RNA to some positively charged lipids in a specific ratio (which results in a specific ratio of charge to mass) causes them to localize to the spleen and then get taken up, translated, and presented by dendritic cells when injected intravenously.
So, put it all together, and the workflow for treating cancer looks something like this:
1. Find a protein produced by the cancer cells that is either sufficiently different from the same protein in normal cells (due to mutation) or not produced in normal cells.
2. Construct an RNA transcript that will produce that protein when translated.
3. Attach that RNA transcript to the liposomes in the appropriate ratio, and inject it into your bloodstream.
4. Let the immune system do its thing.
5. Repeat as necessary to keep the immune response active until it's killed all the cancer.
Obviously step 1 is still the hard part, and the paper chose as a proof of concept two example cancers for which this step was already done. But finding a viable cancer-specific antigen is certainly orders of magnitude easier than determining the mechanism of a cancer and then developing a treatment specific to that mechanism.