Calories “in” vs. Calories “out”

Yes. Calories “in” vs. Calories “out” is an oversimplification of sorts, but calories are still what matter most in order to lose weight.

And as stated in the  infographic, when people eat fewer calories they lose weight and when they eat more calories they gain weight.
This is outlined in The Energy Balance Equation:
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𝙲𝚊𝚕𝚘𝚛𝚒𝚎𝚜 “𝚒𝚗” - 𝙲𝚊𝚕𝚘𝚛𝚒𝚎𝚜 “𝚘𝚞𝚝” = 𝚆𝚎𝚒𝚐𝚑𝚝 𝚐𝚊𝚒𝚗𝚎𝚍/𝚕𝚘𝚜𝚝
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And generally speaking, +/- 500 calories per day equates to roughly 1 pound of weight gain/loss per week.
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It’s also true that different foods affect our bodies in different ways and provide our bodies with different micronutrients (very important for overall health).
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Different types of foods also make it more or less difficult to adhere to a calorie deficit or calorie surplus based on their calorie density, satiety value and overall nutrient profile.
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 The bottom line is that no matter how clean or how flexible your diet is currently, Calories “in” vs. Calories “out” is a mandatory component for changes in bodyweight and body composition.