There is nothing wrong with working in restaurants and cafes in principle, as food and drinks are prepared in them and offered to the customers. It is only haraam to work in them if these places include things which are not permissible, such as:
1. If they offer food and drink that is forbidden according to sharee’ah, such as pork and alcoholic drinks, or if shisha is offered there.
2. If things that are not permissible to be shown are shown there, such as movies, songs and programs in which there is uncovering of ‘awrahs, such as sports matches and wrestling matches.
3. If they allow customers to smoke.
Thus it is clear that working in the cafe described in the question is permissible in principle, but this permission is cancelled out by the fact that customers can watch sports matches in which ‘awrahs are uncovered, and by the fact that it also allows smoking. The people in charge should prevent these haraam things, but if they do not and they use allowing things as a means of attracting customers to the cafe, then working in this cafe is haraam.
With regard to working running a cafe, please see the answer to question number 47396. With regard to the ruling on watching sports matches and sports channels, please see the answer to question number 95280 and 82718.
And Allah knows best.