For topical applications, let's focus on the "Sap" or "Latex" layer as demonstrated in the pictures above.
This layer contains the aloin which is part of the Anthraquinone group of compounds that, among other things, contains powerful anti-inflammatory ingredients.

As can be watched in the links below, the ladies are demonstrating the use of the aloe skin to resolve acne and similar skin conditions: 
Min 3:15, Notice, the lady in the video, is using the aloe skin with the gel - but don’t be confused, by rubbing the peeled aloe skin with the gel against her skin she rubs some aloin with it!
Min 2:26, Same use of the aloe skin peel, 
Min 1:25, Same use of the aloe skin peel,

 

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A new trend among aloe vera fresh leaves users is, to take the fresh aloe vera leaf peeled skin, scrape the gel and the latex from the inner surface of the leaf (using a serrated knife or a grapefruit spoon), and mix it with some additives to apply in cases of various skin fungus conditions. (Read more)
An example for such "recipe":

1. 100 ml of scraped gel,

2. ​10-20 ml of jojoba essential oil or organic, cold pressed coconut or olive oil,

3. 10-20 ml of apple cider vinegar (containing 5% acetic acid),

4. ​10 drops of lavender essential oil,

BOTTOM LINE: DON’T THROW AWAY THE PEELED SKIN!!!, there are those that put the skin in jars and keep them in the freezer, others, simply and keep that gel in jars - one, for immediate topical applications and the rest of the jars,  stored in the freezer to be used in later time.

Back to Father Zago’s recommendations, for similar conditions and many others, they all include the application of the leaf skin to the skin. Describing how to take care of acne,
copied from his book “aloe isn’t medicine, and yet...it cures!” P. 65, "When acne manifests
itself, apply small pieces of the Aloe leaf with their gel part right on the spot where the pimples show up, holding them in place with an adhesive bandage. Overnight, the Aloe will absorb the secretions and free the sebaceous glands without crushing or leaving a scar."
Here is another example, describing how to take care of an abscess, P. 53, "To take care of the resulting condition, cut open an Aloe leaf and, leaving the skin on the outside, apply its internal part – the gel – on the area where the abscess has developed. Hold the Aloe leaf in place with a bandage. Whether you continue with the treatment is up to you. Immediately, you will experience a prickling of the skin, as if from a pin or bee sting. It is normal. It is Aloe expelling the impurities. You have done well. You are on the road to recovery.
The abscess will begin releasing all its contents within approximately three hours. Immediately see to the purification of the area. A lot of pus or bad blood or waste will come out. After cleaning the affected area, again apply the internal part of the leaf over the spot the pus has come out of. In the course of 24 hours, possibly less, you will notice that the infected area is painless and it has already healed. Fast healing? Too fast? It’s because your blood is now a jewel. If the wound has difficulty closing over, it is because of the bad quality of the blood.
A similar description of the use of the aloe leaf's skin can be found on P. 91 of that book, where Father Zago discusses how to treat Dermatitis with topical application.

Bottom line: Aloe leaf peeled skin is doing wonders when applied topically to many skin conditions, provided that the leaf skin is peeled from a leaf when it is really fresh, because anti-inflammation ingredients tend to disintegrate rather fast after the leaf is harvested!. "generally, the aloe leaves will probably start to go bad after 1-2 days".
As with the ingestion recipe, relying on generations of proven results, you don't have to spend a lot of learning before you use the leaf skin for a topical application - start practicing it today, and watch the results, but don't expect results "overnight", it takes time, depending on your age and the condition, improvement takes sometimes more than a few months.