The job of the immune system is to distinguish self from non-self and to seek and destroy any non-self that it discovers. If you want to get the immune system to fight something, you need to get it to recognize that something as non-self, preferably without also forcing it to recognize your own healthy cells as non-self (because then you'd have autoimmune disease). Cancer is an especially difficult case for the immune system because for the most part, cancer cells are your own cells with just a few mutations[1]. The vast majority of proteins produced by cancer cells are the same proteins that your healthy cells produce. They may be produced in different proportions, regulated differently, etc., but they are the same proteins. Even the proteins that mutated could have only a single amino acid change relative to the original. So the difference between healthy cells and cancer cells at a molecular level is much more subtle than the difference between your cells and bacterial cells, for example. It's not impossible for your immune system to identify cancer cells, but it's obviously not guaranteed either. (There's a nigh-untestable theory that a majority of cancers are actually detected and destroyed by the immune system long before they become symptomatic, so the ones we see are just the ones that managed to evade the immune system in their early stages.)

As I've mentioned above, this paper skips the hard part of finding a suitable protein target by picking two proof-of-concept cancer models for which a suitable "non-self" target is already known.

[1] Actually many mutations, but few that affect protein sequences, which are what T-cells mainly look at.