This is political opinion based on proposed policy changes in NYC that haven't happened yet, but we can analyze some of the claims here. It's true that the restaurant industry runs on notoriously slim margins, but the presentation of some of the numbers is lacking nuance. First to note is the sources in the linked article are all from restaurateurs who have a vested interest in keeping their costs down, and they don't cite any third-party sources.
Restaurateur Richie Romero says that "60% of restaurants could possibly close" due to the potential of ending tip credit and bringing tipped workers up to a higher minimum wage. However, Forbes reported on a similar situation—the increase in certain states of tipped worker wages during the COVID-19 pandemic—which tells a different story:
"Using data from Harvard's Opportunity Insights Economic Tracker, the One Fair Wage (OFW) advocacy organization reports that hospitality businesses in the seven states that have abandoned the subminimum wage for tipped workers closed at the same rate between January 2020 and January 2021 as those in states with a subminimum wage."
Of course, this was during the COVID-19 pandemic, so that closing rate was high at 49%, but Opportunity Insights goes on to note that "some of these seven states have had the greatest COVID restrictions of almost any state, but still have not experienced greater decline in open hospitality business rates than other states." This suggests that, in normal non-pandemic circumstances it would be difficult to reach this 60% figure.
Another note is the 10% margin figure—this isn't just for NYC but is the average net margin in the U.S., according to NYU research. Slim margins for sure, but nearly double the industry's 3–6% historical average, according to Toast, suggesting that the industry has a little more wiggle room than they'd like to let on. Restroworks has similar data, emphasizing that "across the U.S., full-service restaurants average just 3–5% in net profit margin, while quick-service and fast-casual formats see slightly healthier returns at 6–9%. To put that into perspective, the average net profit margin across all industries is approximately 8.5%."
Interestingly, regarding the point of Mamdani needing to "work closely with small businesses"—it appears that he does quite a lot, particularly with restaurants—he even made it a point of his campaign. This BBC write-up emphasizes that "he's campaigned at bodegas in the Bronx, taken politicians to an Afghan eatery in Astoria, organised a city-wide scavenger hunt that concluded at his favourite Middle Eastern cafe and consistently championed family-run 'hidden gems' in the city's outer boroughs where many tourists typically don't travel." This suggests that Mamdani makes a point to work with restaurant owners—but perhaps is less concerned about owners with broader large scale operations that span multiple states and is more focused on independent, immigrant-owned, and outer-borough establishments.