I think that sentence shows that Tesla did not quite grasp the results from relativity. This is not unusual, as many physicists required many years to fully accept relativity, but by 1932 (the date of the writing of that text) I would expect it to be already orthodox knowledge.
In any case, Tesla is known to have been a self-taught experimental genius and it's not unreasonable to believe his understanding of fundamental physics was flawed. This does not overshadow his achievements and genius, it just means his talent was not regarding the same inquiries as for, say, Einstein or other theoretical physics.
The best understanding of Einstein's relation is that Energy and Mass can be seen as two sides of the same coin: mass can be converted to energy and energy to mass. Examples:
- Creation of particles at accelerators: energy to mass.
- Annihilation of matter (with anti-matter): mass to energy.
- Mass of nucleons is not the sum of the mass of the (valence) quarks, instead it is the related to the energy of the strong nuclear force confinement.
So Tesla was not right about his interpretation, but then again you have to remember that Tesla was an experimental, engineering, inventor genius and not a theoretical physicist. In fact, he had no formal training as a physicist (not a fully formed field at the time) and only partial higher training in scientific and engineering areas.