Let’s first distentangle that sentence:
- That these skills are transferable is a noun clause and the subject of the main sentence.
- makes is the verb.
- them refers to these skills and is the object.
- especially beneficial is an predicative adjective referring to them.
Now to your questions:
Why makes? (Of course, because of that.)
Actually, it’s not because of that – at least not in the way you probably think it is. That is a conjunction marking the beginning of a noun clause. That that is identical to a pronoun is the nature of the English language is something that you have to live with. There are languages related to English that allow for analogous structures but have a distinct word for this purpose (e.g., German has dass).
That makes has a singular s is plainly due to the fact that noun clauses are treated as singular by the English grammar.
But, does that mean something – the fact?
That is a conjunction and has a grammatical function here, i.e., it informs the reader about the grammatical structure of the sentence. It has no real meaning of its own, e.g., it could not be easily translated to an arbitrary other language (though analogues exist in other languages with a similar grammar, e.g., the German dass).
That being said, you can replace that with the fact that, the circumstance that, the concept that, or something similar in such a situation to approximate the meaning of the sentence or as a help to understand it. Note, however, that neither of these choices is accurate in every context, e.g., the noun clause does not need to describe a fact.
Can we put that in other places in this sentence?
No. English grammar demands that conjunctions are located at the beginning of dependent clauses. You may not even move the noun clause (at least without further modifications) as it is the subject and these have to be at the beginning of a sentence. What you can do is using it as a “placeholder” (expletive) for the noun clause and move it to the end of the sentence:
It makes these skills especially beneficial that they are transferable.
Note that this shifts the emphasis of the sentence.