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 Dictionary
Dickensian
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."