When cooking Chicken Tandoori or Chicken Kababs, how do you make that crisp spicy layer thicker?
Restaurants usually make it on charcoal grill. I don't know the science but that does make a difference in achieving that look as well as taste. Use thicker yogurt with higher fat level, and keep the marinade thicker. I have been able to achieve that crusty layer by keeping my marinade thicker and using yogurt with at least 5% fat. Low fat yogurt usually results in thinner marinade.

For red color, you can use either red/deep orange food color or paprika. In south asian cuisine, we would often use something called 'Kashmiri red chilli powder' which is a mild chilli pepper but brings a gorgeous red color.

Edit: To add more from comments

The list of ingredients in the recipe you've linked is exactly what we usually use. There is no additional ingredient to that. Only the quality of ingredients and cooking technique will make difference in the results. I usually cook on a Gas mark 6. If you're washing the chicken and then using it straightaway, I find that it leaves the chicken too wet and it doesn't hold the marinade very well.

Also, if the chicken is a bit watery inside before marinating (like it becomes if left soaking in water for a while), it releases a lot of water during cooking which makes the marinade layer come off. I drain my chicken in a metal strainer for roughly 10-15 minutes before mixing in with the spices, regardless of frozen or not.

Similar happens with low-fat yogurt which is more liquidy and runny than high-fat yogurt. If you do have to use low fat yogurt, try straining it like the recipes asks for thick strained curd. By straining you're removing the liquid which will help the marinade to stick together well. Greek yogurt will also work.