Technically, no, you don't need a license for CrystalExplorer, but if you use the app, these are the conditions:
You must be conducting research for peer-reviewed publication at a bona fide degree-granting institution to qualify.
You must not use the free version of CrystalExplorer to conduct commercial research, confidential research, or research that is not likely to be published in a peer-reviewed publication.
If you publish research including results from CrystalExplorer, you must cite CrystalExplorer as described here.
CrystalExplorer is provided as-is, and without warranty of any kind.
For additional information, visit the Licensing page on the official website.