The clinical trial for the treatment you're talking about is on ClinicalTrials.gov here:
https://clinicaltrials.gov/ct2/show/NCT03410901
It says the trial started in April 2018, and is expected to end in October 2020; these estimates are sometimes off and it's possible other things like the COVID-19 pandemic could impact the timeline, as well as unexpected difficulties in recruiting patients. The study also seems to still be recruiting - unless that is inaccurate and out of date, the October 2020 timeline seems quite ambitious and probably won't be met since their primary outcome is over 8 weeks. Additionally, that's the end of data collection only for the primary endpoint. Their secondary endpoint includes 96 week results, so if they want to complete the secondary endpoint before publishing they would possibly have another couple years to wait (alternatively, they may publish with what preliminary secondary data they have). Data analysis and publishing can also take several months after that.
This study is a Phase 1 study, the earliest type of clinical trial. Approval typically occurs after much larger Phase 3 studies are completed. Most treatments fail at some phase of study, even if they have been shown to work in animals. Cancer is a relatively slow disease, so studies of efficacy in cancer may need to be longer than for other diseases if they intend to show positive outcomes over multiple years. In total, 10 years sounds like a pretty fast pace to go from preclinical data to clinical approval; it looks like APC8015/Provenge was approved about 6 years after the first Phase 3 clinical trials started.
Note that this study is not really a cancer vaccine, vaccine is in "quotes" in the article you linked, which suggests it's more of a metaphor. In this case, the "vaccine" is a combination immunotherapy. It is meant to get the immune system to target cancer cells, but it's not a vaccine in the typical sense used when talking about pathogens. This particular therapy also is intended clinically for use against a specific cancer: B-Cell Non-Hodgkin's Lymphoma. It's not a generalist cancer treatment, but the article you linked to suggests they are hoping that a couple other specific cancers might also be treated in the future. The only true vaccines I am aware of that prevent cancer are those targeted to oncogenic pathogens like HPV.
