Whoever comes first

[Nonverbis]

Please always give the title and author of any book you quo

It is that book by Kobrina, just next page.

are the subject of the sentence.

No. This is a case of a relative clause. Just a case of ellipsis here.

Whoever gets there first, [they] should keep seats for the rest of us

Proof (source The Oxford Dictionary of English Grammar by Aarts B., Chalker S., Weiner E):

 

[5jj]

the underlined words are the subject of the sentence.

No.

YES.

Once again, the page you gave us does not contradict anything I have said.

 

[Nonverbis]

I can't understand your point of view at all. As far as I remember you have been criticizing me and have not given your own explanation.

Let us return to the initial question.

Whoever gets there first should keep seats for the rest of us.

This is a case of future action.
Future in English is expressed by a limited number of means (will, is going to etc.).
And if you choose a means wrongly, there will be a mistake.

You don't like my explanation. But I have been trying to the best of my abilities.
But at least I have tried. Maybe your explanation is better?

But as far as I remember, you joined the opinion of jutfrank that there's nothing really to explain here.

 

[jutfrank]

No. This is a case of a relative clause. Just a case of ellipsis here.

Whoever gets there first, [they] should keep seats for the rest of us

That's incorrect. As 5jj says, Whoever gets there first is the sentence subject.

The whole sentence is an independent clause. Sentences that express concession typically consist of two clauses, one of which (the subordinate one) is concessive to the other. That's the case in the example sentences described in the grammar books but not in the case of our original example here. Concession needs two things to be contrasted.

Although he's quiet, he's not shy.

The subordinate clause above is concessive. It has a logical relation to the main clause. That's what we mean by 'concession'.

 

[Nonverbis]

I believe, our discussion has got a cyclic character. At least, I don't seem to be able to add anything new here.

 

[probus]

By the way @Nonverbis "between a blind and a deaf" is incorrect because both blind and deaf are adjectives, not nouns. You need the word "person" after both blind and deaf.