No. Khomeini was the first to apply it as a
political doctrine (ie, a theory of statecraft, rather than of strictly religious law), but as a Muslim religious term it predates him by over a century.
Murtada Ansari (d. 1684) was the first person to come up with the idea of "rule of the jurist", or velayat-e-faqih.
And even now, Khomeini's interpretation is not the only interpretation. Grand Ayatollah al-Sistani, the foremost Shia Islam cleric in Iraq, favors a
much more limited version than that found in Iran:
In other words, far from being the supreme and absolute authority in all matters as in the Khomeini model, a faqih (Leader) has authority over religious issues only, and when it comes to "social order" matters any decisions regarding that have to be accepted by a majority of the community, and if the community tells the Leader to stuff it regarding any particular non-religious issue, then he has no "guardianship" over the community. Combined with al-Sistani's declaration that women not only can vote, but
should, and his actions in Iraq to keep religious matters separate from the secular government being established, that makes his view of velayat-e-faqih almost exactly the opposite of Khomeini's.