More important than strategizing and planning in the headquarters, the biggest CHALLENGE of owning a restaurant is making sure staff treats the customers well and the chefs prepare good food. "Battle" is a type of challenge. A lot of times, business executives spend a lot of time in meetings discussing business plans and strategies on how to increase profits, but they don't always understand what is actually happening in the stores/restaurants. None of those meetings mean anything if staff and customers don't enjoy the experience.

I guess he means that the most important conflicts in our lives happen in restaurants, like informal business meetings or even wedding proposals. But its just a guess.

What part of the sentence do you not understand?

A battle takes place in a war, in English, battles are a metaphor here for conflicts. Conflict takes place for the business to survive and win. You are fighting and giving your all in the battle for high quality products and excellent service. Its the people working with the customer, he/she says, not the managers with a lot of words, the frontline. The people that provide that end result directly with the customer are important in his evaluation.