I googled and tried to search words like gigantesque, alienesque, and animalesque so that I could know whether they are informal or redundant forms of giant, alien, and animal, respectively. But not even a single dictionary had references to such words.
See the pattern (the words include the suffix -esque):
gigantesque > giant
alienesque > alien
animalesque > animal
All of these pairs are of adjectives; what's the difference? Are the words suffixed with -esque not redundant?
Your "animal" and "alien" examples have the suffixal morpheme -esque added to an existing English word.
-esque
In the manner of; resembling:
American Heritage Dictionary
The giant example is a bit different in that it came into English in the early 19th century from another language, most likely Italian "gigantesco", adopted as "gigantesque".
I'm assuming you're not asking why there are multiple words for the same thing generally, such as why do we have "boylike" and "boyish", or "girly" and "girlish". I'll focus specifically on suffix -esque. I assume your question to be asking why, if "giant" can be used as an adjective to mean "giant-like" or related to giants, and "alien" can be used as an adjective to mean "alien-like" or related to aliens, then why would you add -esque to these words if it seemingly means the same thing?
To begin with, I can't find a definition of "animalesque", so I can only assume it means exactly what it looks like, ie., something akin to "animal-like". An entry for "alienesque" I found in Wiktionary, which simply defines it as:
1.Suggestive of an alien.
Link
This is a very simplified definition, as alien can mean quite a few things. Most dictionaries go into descriptions meaning "foreign", "strange", "extraterrestrial", etc.
As to how these words come about, the suffixal morpheme -esque is very productive (see productivity). In terms of morphemes (word parts) it means that they are word parts freely added in a spontaneous or even improvisatory way to change the meanings of words. For example, prefix un- is highly productive. You might have a cat defanged, then you might say the cat is unfanged, even though "unfanged" isn't listed in nearly all dictionaries, and you could argue all day whether it's a word or not. That's how words like this come about, adding parts to words when it makes sense to do so.
As words' meanings are concerned, when they end in -esque, it mostly just means what the definition I gave above says. However I'm sure you know words take on particular meanings over time. I'll give a couple of examples. RegDwigнt brought up Kafka. If we look at some definitions of Kafkaesque we can see some meanings that go beyond just "Franz Kafka-like":
kafkaesque
2. Marked by surreal distortion and often a sense of impending danger:
American Heritage Dictionary
statuesque
statuesque
like or suggesting a statue, as in massive or majestic dignity, grace, or beauty.
Random House Kernerman Webster's College Dictionary
Here we can see a meaning more than just statue-like, it's hinting at grace and beauty.
picturesque
1. visually pleasing, esp in being striking or vivid:
Collins English Dictionary
Again, goes beyond just meaning like a picture.
Same thing goes with other word parts, I'll just give one example of -ian:
-ian
suff.
1. Of, relating to, or resembling: Bostonian.
American Heritage DictionaryDickensian
2. (resembling or suggestive of conditions described in Dickens' novels, esp)
a. squalid and poverty-stricken: working conditions were truly Dickensian.
b. characterized by jollity and conviviality: a Dickensian scene round the Christmas tree.
Collins English Dictionary
As far as I know "alienesque" or "animalesque" haven't taken on meanings beyond what you would expect from analysing the noun and the well known -esque suffix.
Is it redundant to add -esque to alien or animal? One is using a noun which is widely accepted to be also an adjective, and the other is using the noun and attaching a suffix to create an adjective meaning "related to or resembling" the noun. Is there a difference?
"animal instincts"
"animalesque instincts"
"alien technology"
"alienesque technology"
As you'd expect the alienesque and animalesque adjectives mean alien-like and animal-like. Alien and animal adjectives mean "of aliens" or "of animals".
However the distinction isn't so clear in some cases. For example, consider the difference between "He has animal instincts" and "He has animalesque instincts." As the adjective "animal" can mean "characteristic of animals", then:
"He has animal instincts."
seems to me to be the same as:
"He has animalesque instincts."
Addressing the specific example, "alienesque" implies that the thing being described somehow resembles an alien thing or gives one the sense of seeing an alien thing. But, the implication is, the thing is not actually "alien" in any literal sense.
According to the Oxford English Dictionary (https://www.oed.com) the suffix -esque comes from French and to French from Italian -esco. In words that are borrowed from French the ending is said to often have the sense of "resembling the style partaking of the characteristics of".
This resembles the sense given in Merriam-Webster (https://www.merriam-webster.com), "in the manner or style of", as well as that of Etymonline (https://www.etymonline.com):"resembling or suggesting the style of".
The Oxford English Dictionary does give another sense as well, however. According to OED the most common use of the suffix -esque with already existing English words is when the writer or speaker has a need to create a new word for the situation. The suffix -esque then brings an element of playfulness to the expression, with the sense that both the speaker (writer) and the listener (reader) know that the word does not exist in any standard vocabulary.
