The RPG-7 uses an initial explosive charge to propel the rocket a safe distance away from the soldier who fired it, before the rocket ignites as takes the RPG the rest of the way. Otherwise the soldier would get a face full of rocket exhaust.
On the first test at around 1:16 you can see the rocket is lit.
On the second test at around 3:59 you can see the rocket motor failed to ignite.