Or is the calories (kcal) the only relevant piece of information when looking at food labels?
Fat content is relevant to your overall health, and so is the rest of the information on food labels, but in terms of counting calories, no.
So for losing weight I don't need to pay attention to the fat content or anything else, just calories?
Technically, if you burn more calories than you eat (regardless of fat, carb, or protein content), you will lose weight. There are a lot of diets out there such as low carb or low fat and they all have pros and cons. For example, I like low carb diets because the protein and the fat keeps you full, and I lose weight more easily on low carb diets. However, I am a carb addict, so it's really hard for me and may or may not be sustainable in the long term. Do some research and see what would be sustainable for you.
The only thing is, losing weight isn’t the only thing in life. We eat to fuel our bodies and sustain our lives and health. If you eat too much of your calorie allowance in fat, there won’t be enough calories left in your daily allowance to get the other nutrients your body also needs.
it's true a calorie is a calorie is a calorie...however, a good rule of thumb is to try and keep your fat calories below 30% of your total daily calories