No - this is not WWIII. WWIII will take place after the destruction of Damascus (Isaiah 17:1), and Russia, China and all the Muslim/Arab nations come enmasse to take Israel out once and for all.
What Russia/China/et al do not know is that God will be waiting for them - and God knows how to "throw rocks".
Read about it in Ezekiel 36-39. These scriptures also indicate that Communism and Islamism will die at the end of that war and it will usher in the final harvest for the Church!
So who says the numbering of conflict called "World Wars", a purely secular exercise, should have anything to do with your reading (or misreading) of the Holy Scriptures?