Yes, this product contains milk, egg, and gluten, so it is not suitable for anyone avoiding those ingredients. Because the protein sources are whey protein isolate, egg protein, and milk protein isolate, it is also not suitable for a vegan diet. It may be compatible with a vegetarian diet, but read the complete ingredient list before you decide.
It also contains sweeteners and dietary fibre from chicory and isomaltooligosaccharides. The product information does not present it as sugar-free; it only says that the carbohydrate content is relatively low and that the total sugar and calorie load is moderate. If you are sensitive to sweeteners or follow a plan that restricts certain types of fibre, check the allergen and ingredient section on the package first.
The milk-cream filling is a source of milk protein, so those with a dairy sensitivity should not assume the filling is dairy-free. Since formulations can change, the label on the specific package is the most reliable source if you have a food allergy or intolerance.