Alright, I would've responded last night, but I was stuck waiting for my account to be activated by the mods.
I think the most significant happening if the Habsburgs were essentially erased from history would be where that would leave Austria and who would lead the Holy Roman Empire. Duke Frederick II of Austria was the Babenberg in charge of the Duchy of Austria, which had been ruled by Babenbergs since about the 12th Century. The Babenberg's conflicts with the neighboring Kingdom of Hungary finally resulted in the Duke Frederick II getting killed during the Battle of the Leitha River. This effectively extinguished the Babenberg family as they had no remaining male heirs. Nearby, in Bohemia, King Wenceslaus tried unsuccessfully to gain Austria diplomatically by marrying his heirs into the remaining female Babenbergs. Gertrude of Babenberg married Herman VI of Baden, ruining Wenceslaus's chances until Herman VI died in 1250, at which point Wenceslaus invaded Austria. He released his son in 1251 who he had imprisoned due to a noble rebellion not long before, and he appointed him Governor of Austria as well as Margrave of Moravia. The Austrian nobles appointed him as Duke of Austria and he married Maragret of Babenberg to strengthen his rule. When Wenceslaus died in 1253, Ottokar became King of Bohemia. After strengthening his influence and power in Europe for many years by carrying out different wars and alligning himself with certain people, Ottokar II was one of the most powerful men in Europe. At this point, Ottokar's next goal was to win the title of Holy Roman Emperor, something he was unsuccessful in in OTL as Rudolf of Habsburg won the title in 1273. As OTL goes, Ottokar isn't happy, starts a war, loses, and Habsburgs gain control of Austria, badda bing badda boom.
Here's where we diverge from the OTL. Without any Habsburgs in his way, Ottokar II is elected Holy Roman Emperor. As Holy Roman Emperor, assuming he doesn't piss anyone off, he establishes the Premyslid Dynasty as the most powerful family in the Holy Roman Empire. From here, any number of things could happen, but it's really difficult to speculate as it's too early on for many accurate predictions, and there's no way of knowing what sorts of characters would be born of said dynasty. Perhaps they would be crushed by the Ottoman invasions and Europe would be devastated. Perhaps they would have all of the strength required to keep the HRE under control during the Protestant split. I couldn't say how Spain would unite, if at all, without Habsburg rule. After Ferdinand and Isabella died in OTL, Philip I of the Habsburgs ascended to the throne of Castile. Perhaps without this happening, Henry VIII of England never would have married Catherine of Aragon and instead would have married her older sister, Joanna of Castile. Perhaps this wouldn't have happened, since Henry VIII was a friend of Philip I and this friendship greatly influenced his marriage choice. Since Habsburg Spain was one of the most expansionistic of all of the Spanish monarchies, it may be that Spain's colonization of the New World was not nearly as extensive as under the Habsburgs.
There's other ideas, but I kind of got to the point that I didn't feel like writing anything else, but essentially many of the events that helped shaped the modern world either changed drastically or didn't happen at all. Kind of crazy to think about how important the Habsburgs were.