This requires a magically flexible definition of "market" at very best.
The smallest number of competitors that can split market share such that none exceed 15% is 7, and that cuts it absurdly close for an existential risk.
Do non-profit organizations count for this rule? If not, how would corporate structures that intentionally obfuscate these distinctions, e.g. IKEA, be handled?
If there's not some extremely tricky qualifiers, these markets seem likely to be a problem, just for starters: medicines†, operating systems, utilities to a specific house or even city, spy satellites, chemicals that are difficult or dangerous to synthesize, combat aircraft, crewed spacecraft, EUV lithography, armored fighting vehicles, cellular telecommunications services, samples of organisms restricted to high biosafety level labs, and literally any new product category. † Imagine a serious condition getting its first drug treatment approved and the company saying "Only every seventh patient is eligible." Also, no one could offer a specific specialized surgical procedure until seven or more independent organizations in the same geographic area have qualified staff and equipment, which would be especially hard for any novel techniques; if the problem it addressed was rare, they'd also effectively be forced into a cartel to allocate the patients evenly.
There's also separately and unavoidably the massive problem of transitioning from the current situation to one compliant with these restrictions.
Edit: Switch to using a dagger for the footnote to avoid a formatting issue.