I am by no means an expert in EU antitrust law, but I believe the relevant EU case law for "market dominance" is something like 40% of the EU market (Which Apple doesn't have in the EU smartphone market). The DMA defines gatekeepers based on annual revenue (either 7.5 billion in the EU or 75 billion globally) and number of EU end users (45 million monthly, or 10,000 annual businesses).
This European law professor noted that the law seemed intentionally written to exclude Spotify:
(Also of note, iPadOS doesn't meet the quantifiable definition to be covered by the DMA but the EU said "doesn't matter, the DMA applies anyway" - maybe that's one of the "spirit of the law is clear" things I keep getting told when I point out the law isn't clear.)
In general, I would assume if something could be addressed under current law, it would make more sense to do so than write an entirely new law, but I also know passing legislation is easier in the EU than in the US, so maybe that is less of an issue than it would be here. In any case, unless I see evidence otherwise, I am assuming the EU is changing the definition of market dominance that they use in other markets because they're trying to target companies that aren't necessarily dominant under that definition. Which again, is their right to do, but we don't have to pretend that they're not doing so in a way to avoid targeting European companies - despite their protests that all they care about is protecting competition.