The article says they've raised $115 million to deliver in 4 cities. The populations of those cities are:

San Francisco: 837,442

New York City: 8,400,000

Seattle: 652,405

Greater Los Angeles: 3,800,000

For a total of 13.6 million people, or $8.45 per person.

I looked at one example by finding an SF zip code, and found they were charging $10.95 for 650 calories(if you assume 2000 calories, you might say they're looking to raise $10.95 at a $33.69 daily food valuation). It's also 59 calories per dollar:
https://munchery.com/menus/sf/#/0/dinner/bbq-pork-with-rice-...

I checked a couple other zip codes, and they do seem consistent with $30-$34/day in food 'valuation' by calories.

Looking at San Francisco, it looks like people spend an average of $3,937 to buy 48% of their away-from-home food(2000 * 0.48 * 365 / 3937 = 89 calories per dollar), and $4,215 on 52% of their at-home food(90 calories per dollar)
http://www.bls.gov/regions/west/news-release/ConsumerExpendi...

So their food is about 50% more expensive than the average in the region, per calorie. If you assume people's expenditures rise with their income exactly, and that the average income in San Francisco was $92,780 from that same link, then you'd expect them to be targeting people who make 1.5 * $92,780 = $139,170 which is the 74th percentile in San Francisco. Applying this uniformly reduces the 13.6 million audience to 3.264 million(edit: Not sure you can apply a percentile like that).

I'm not sure what their markup is, but if you assume it's the 50% rather than them simply choosing more expensive restaurants, then they need to generate $3x in sales to generate $x in revenue. So $115 million / 3.264 million = $35.23/person * 3 = $105.70/per person on average to make revenue equal to their investment. If you assume only 10% of its target audience ends up using Munchery, then this rises to $1057/person, or about 96 overpriced meals. They appear to outsource all the actual work to restaurants, but they might get a bulk discount. Maybe that's eaten up by their operations.

You could reduce this by a factor of f by assuming that the valuation was some fixed multiple f of their valuation. I've heard 3 is common for f, and probably these are preferred stock so the multiple might be higher.

I don't know - it seems like the average yuppie would have to buy way more overpriced delivery Chinese food than I expect is reasonable for their business to make sense. My historical credit card statements show about $6/day on all my food, compared to their 'valuation' of $33.69.

I'm not sure I understand where the investor money's coming from though: It's traditionally hard to get money for a restaurant(loans require higher down payments, etc.) since they tend to lose money. Buffets tend to be more efficient than sit-down restaurants like they indicate here, and I've also seen some restaurants hire delivery staff. If they sold it to investors as "We want to set up a couple buffets three times as big as average with some delivery staff instead of a sit-down area", I can't see them actually raising the money. (The 3x comes from me looking at a local buffet in Portland, which was 11,000 square feet, and comparing it to the 30,000 one mentioned in the article. Admittedly theirs probably doesn't have any sit-down room).