I believe the problem is that you no longer should have defaults in the environment.yml for a channel, following the example for Conda environment with environment.yml.
I just made a fork of the Parcels repo and made that change. Not only does it get past that step and launch a session, the parcels_tutorial.ipynb notebook that comes up at launch runs all code cells successfully. Fork is here. Try to launch directly by clicking here.
Plus, I had set up an unrelated one using that as a template recently and it worked here.
The JupyterLab sample repo listed on the sample repos page in the Binder documentation uses requirements.txt and not environment.yml. The one I reference above is for use of environment.yml.
The one you reference hasn’t been touched by a human in over a year and perhaps more importantly, is not the one the Binder folks offer as a guide.