No. Your source makes clear that Marconi sent the first message (Tesla failed to send a radio message in 1895, Marconi succeeded). Read "My Father Marconi" by his daughter Degna. Fantastic book.

Other than that, a very fascinating read, the link you shared. Patent stuff is silly, but were way less silly back then, and had more positive 2nd order effects back then.

It was cool how Tesla and Marconi held each other in high regard, and built on each other's works.