EF source says: [FONT="]'That' is often used to introduce defining relative clauses when they follow the words [/FONT]something, anything, everything, nothing, all[FONT="] or a superlative. It may be omitted when it is not the subject of the clause.
I don't see how adding "that are" changes the meaning or improves understandability. In general, good style favours the briefer of two equivalent options. In my opinion, therefore, the passage is better with "that are" left out.
Nothing has been omitted. The underlined adjective phrase is a post-head modifier of "antigens systems".
We could also have Antigens systems that are important in transfusion, where the underlined element also modifies "antigens systems", but this time it is a relative clause, not an adjective phrase.
There is no difference in meaning between the two constructions.