The idea is gamers come to the gamer cafe, have their concessions and uses the tables for the evening. Games in this theoretical model are purchased online, because duh, while the brick and mortar business provides the venue and food. If there are games for sale, it's like the pro shop in a bowling alley. It's there. Some things are bought, but it's all about the lanes.
Unfortunately, this doesn't jive with reality. If we're going to eliminate the brick and mortar game product sales, something else has to give. If we can't turn inventory, we have to turn tables. You gotta turn somethin'. You're not going to turn tables with a bunch of gamers camping out playing Tikal for 90 minutes while drinking Americanos. There's no money there. You certainly don't have gamers stacked 3-4 deep to play, either, although we can hope the hobby continues to grow.
Most cafes need turns on tables per night like game stores need turns on games in a year, probably around 3-4. That means 3-4 customers per table come in, purchase concessions, eat them, and then get the hell out. And those tickets need to be a lot more than two bucks a person for a cup of coffee, preferably around $15-20. If you've got a fancy restaurant, you may turn your dinner service just once a night, but your ticket is going to be much higher than that $15-20 average.
If a location appears to be breaking this rule, it's most likely because they're running a very good coffee shop by day, and a gamer cafe by night (like GameHaus Cafe in Burbank). Running a gamer cafe in the evening is kind of ingenious, since it's when most coffee shops are closed. I know locally of a coffee shop planning to open a coffee shop/bar combinations, since the coffee shop is empty at night. You pay rent 24 hours a day, so why not? This model really isn't a gamer cafe, it's a gamer themed cafe, and if you ask the baristas at GameHaus, they'll tell you flat out, this is a cafe, I know nothing about this board game nonsense (paraphrased).
You're now in the coffee shop business (gamer themed) which means you're going to have to run a very good coffee shop to make this work. Just like if you add a coffee kiosk to your game store, you are very much still running a retail game store with some coffee, and you'll have all the issues with retail. There are full fledged hybrid models out there, with Mox Boarding House and Cafe Mox being the most interesting, as they run both models quite robustly.
However, in these models, you're essentially running two businesses side by side. You've got a great bar/restaurant in a great retail establishment. Although it's a clear win when we look at Third Place Theory, you have to wonder if each piece of this puzzle would be more profitable if you separated them. That's often the case with hybrids. Clearly you need top expertise in both business segments to be successful and if you lack in either, the impression of the entire business suffers. A bad waiter can ruin your game store and a poor game store manager can trash your bar. Could they be even more successful separate?
Also don't underestimate what it costs to hybridize a game store. A coffee shop build out is easily $40,000-$60,000, while a restaurant could run you $150,000-$250,000 and up. That looks suspiciously like the cost to open another store, and if you've made it to this point in your business, opening and running game stores is your skill set, not making Americanos and serving customers four times your usual speed.
Anyway, bottom line is there is no magic bullet. There is no pro shop model that works. You're either turning game product or tables, or ideally both. But not neither.