More precisely, Duke Francesco V of Modena in his last will appointed as his heir Archduke Franz Ferdinand, under condition that he assumed the surname of Austria-Este (and not of Habsburg-Este, as it is often reported). In case Franz Ferdinand predeceased Duke Francesco or in case he wouldn't accept the condition, the heir would be the next younger brother of Franz Ferdinand, under the same condition (and in case any of the sons of Archduke Karl Ludwig couldn't inherit, the heir of Duke Francesco would be in equal shares his nephews Don Carlos and Don Alfonso de Borbon).
In 1875 Duke Francesco died and Archduke Franz Ferdinand became his heir, and therefore assumed the title of Archduke of Austria-Este. In 1900 he married morganatically, so his descendants were inegible to inherit his titles. So his heir presumptive became his brother Otto. Otto died in 1906 and then the heir presumptive became his son Karl.
In 1907 in his will Archduke Franz Ferdinand appointed Karl as the heir to the Modena inheritance, under the condition that he assumed the surname of Austria-Este.
After the death of Franz Ferdinand in 1914, Karl therefore assumed the name and the arms of the House of Este and became Archduke of Austria-Este.
He also became Emperor in 1916. So in 1917 he decided to transfer the title and rights on the Este inheritance to his second son Robert (and not to the eldest son Otto, because Otto was the heir to the Imperial throne), and in turn Roberto assumed the title of Archduke of Austria-Este. The same title is currently used by his children and male line descendants.