Etymology: Latin, < Greek θησαυρός a store, treasure, storehouse, treasury.
1. Archaeol. A treasury, as of a temple, etc.
a. A ‘treasury’ or ‘storehouse’ of knowledge, as a dictionary, encyclopædia, or the like.
b. A collection of concepts or words arranged according to sense; also (U.S.) a dictionary of synonyms and antonyms.
c. A classified list of terms, esp. key-words, in a particular field, for use in indexing and information retrieval.
I didn't realise the word meant treasury, but that leads us to
Etymology: < Latin thēsaurārius (see thesaurary n.) + -al suffix1.
Of or pertaining to the office of treasurer.
Cheifly Sc. Obs.: The treasury; the treasurership.
OED doesn't list a canonical adjective for "of or pertaining a dictionary of synonyms", but it would be possible to coin thesaurial from thesaury which is sufficiently like thesaurus to be intelligible, and which introduces neither the extra syllable of thesaurarial nor the -c- in thesaurical.
I guess that New Scientist coined thesaurical because of its similar sound to rhetorical, but that is to misuse the -ical ending. The base word does not end -ic.