The cold war included:
vietnam war
korean war
soviet-afghan war
iran-iraq war
bay of pigs
various central american civil wars and military actions
berlin air lift
and probably a few others I’m forgetting.
proxy armies fighting here and there and other low level conflicts don’t add up to a real world war. Otherwise you’d attribute world wars to Alexander, Napoleon and a lot of other people throughout history.
A real world war would be NATO vs Soviet Union directly. The best of the best vs the best of the best. That war would’ve been very costly and would’ve certainly involved the use of nukes.
I don’t even think this whole “war against islam” could be considered a world war. Iraq had the strongest army of all the arab/muslim countries and it didn’t take that long to fall.
What I am really concerned about is if North Korea and China somehow joined forces and declared war. They are the ones with the most developed military compared to any of the other bad guys (Syria, Iran, Cuba, Venezuela, etc)