It could work for niche stuff, but energy costs is always what kills these ideas for the mainstream market. Sunlight is free. If we had Mr. Fusion maybe it could work.
Edit: I suppose it could work in the Middle East too where energy may be cheap enough (solar, cheap gas) vs. the cost of shipping it from Europe or further away.
With unlimited power, everything changes. We get the incredible luxury of scientifically produced vegetables. They can be optimized to perfection in harmony with consumer tastes. Every season brings a new designer crop...
Well, maybe it could happen without unlimited power. We can dream.
http://www.caiso.com/TodaysOutlook/Pages/supply.aspx
Around noon PST you'll see upwards of 11GW of solar. (This includes rooftop installations if they have smart meters.)
Of course it's more efficient to just put the plant's leaves in the sun, but water isn't free either and you lose far more water that way. I wonder if cost of water in the desert could outrun the cost of indirect solar -> electricity -> calories? It could be true in the US Southwest, but it could definitely be true in Dubai or Saudi Arabia. In places like that desalination is one of the only sources of fresh water, and that's likely more energy intensive than indoor farming.
So yes it could work in a few markets, but it's not going to replace conventional agriculture broadly.
7.5 people per floor isn't a lot and it's very expensive. Maybe useful for colonizing Mars where money isn't that big of a deal, but definitely not feed-the-world level scaling.