What does "open up" mean?

Compatible standards, allowing other devices/platforms to interact with it, etc. Very common stuff for electronic and computer devices. Sometimes standards emerge on their own, sometimes standards are set by government, sometimes companies try to use their market power to create "walled gardens" and the government steps in to prevent them from doing that. Pretty basic exercise of governmental authority to regulate the products and services offered within their jurisdiction.

If the commission decides Google is in “non-compliance” with the DMA, it can issue a fine of up to 10% of the company’s annual global revenue. But officials have said that they want to avoid issuing blockbuster fines and instead negotiate with companies to get them to comply.

Yeah, the same theory that underlies the doctrine of punitive damages here in the U.S. The government reserves to itself the power to impose a whacking big fine or penalty, so that even the wealthiest folks who violate the law won't just write off a smaller penalty as the cost of doing business.

Again, it's basic governmental sovereignty. Countries get to set the rules in their country. It's not just for immigration and border controls, doncha know - it covers everything that foreigners might want to get up to in their lands. Like, say, a foreign company like Apple or Google that wants the freedom to go into their marketplace....but not play by the local rules? Not going to fly, to borrow your expression....