I voted no, they wouldn't exist in Elder Scrolls if it wasn't for LotR.
But....
....But would orcs exist without a cinematic trilogy like Lord Of The Rings, and would they look like that....
Like others I object to the word "cinematic" meaning the films. I haven't played them but I believe Orcs were in Elder Scrolls games that predated the movies.
Also Orcs in elder scrolls are not at all like Orc in Lord of the Rings, and don't have the same backstory either. But I do think Elder Scrolls Orcs are LotR inspired in some sense.
Of course Orcs also predated the LotRs books.