The Warcraft universe is actually a timeline multiverse, so when Garrosh goes back in time he doesn't really go back in time, he travels to a different universe inside that multiverse.
So in the 'Iron Horde' timeline, the orcs won't invade their Azeroth, Thrall will grow up to be Go'el, Chieftain of the Froswolf Clan, not Warchief of the Horde. Varian will not become a Gladiator. All these things will definitely change in their Azeroth, but 'our' Azeroth, the one where Grommash did drink the blood of Manaroth, Go'el was raised by humans under the name Thrall, did become the greatest leader Azeroth has ever seen, this timeline will remain the same, because it is a different universe, and the only thing the Iron Horde can change in it is the present.
Interestingly since their timeline has now been altered, their Azeroth will never know of Orcs and Dranei, and the fate of their Azeroth may be a lot different for it. The Alliance was formed to combat the orc invasion, if the races of Azeroth never band together, will they be able to stop the scourge? And even if they can, Deathwing will still awaken, and without Thrall as Earthwarden, he will not be stopped. So Garrosh most likely causes the destruction of their Azeroth by trying to destroy ours