They are gerunds.
The words eliminating, communicating, publicising and allocating in the quoted sentence are followed by bare NP complements that act as their direct objects ("the secrecy surrounding pay", "everyone's remuneration", "performance bonuses" and "annual salary increase" respectively). Usually, this is only possible with a verb. For example, the word elimination is clearly a noun, and we can't say *"Elimination the secrecy surrounding pay"; the complement would have to be marked by the preposition of: "Elimination of the secrecy surrounding pay." There may be a few exceptional participial adjectives that can take bare NP complements (such as unbefitting in contexts like "very unbefitting the dignity of such grave personages") but they are very unusual.
"Eliminating the secrecy surrounding pay by openly communicating everyone's remuneration, publicising performance bonuses and allocating annual salary increase in a lump sum rather than spreading them out over an entire year" acts as the (compound) subject of the quoted sentence.
A verb in the -ing form is called a "gerund" when it is the head of a phrase/clause that is used as the subject or direct object of a clause, or as the object of a preposition. It is called a "present participle" when it is used to modify a noun. Some linguists have argued that it is not actually possible to clearly distinguish between gerunds and present participles, and therefore prefer to use the term "gerund-participle", but that's a side issue, since you only asked about how to distinguish gerunds from participial adjectives.
A participial adjective, such as “exciting” in “a very exciting day”, cannot take a direct object. Furthermore, a participial adjective cannot act as the subject of a sentence.