It doesn’t sound any different from what Apple is currently doing in the EU, and that seems to have gotten some measure of grudging acceptance. Though the EU has been known to “creatively interpret” the DMA when it suits them, so who knows.
Apple also still retains the ability to decide which apps to approve or block in the EU, even for third party app stores. If push comes to shove, I suspect the EU government will be making similar “requests” of Apple as well.