I believe it is a subject complement, what used to be called a predicative adjective. Game over is really a kind of contraction of The game is over.
Elsewhere is an adverb.
Another is a determiner.
The word 'over' in the phrase 'over 3 hours ago' is an adverb. The word can also be a preposition, an adjective, an interjection, and a noun. Like many English words, it has multiple functions and meanings. Do not make the mistake of thinking that it must be a preposition unless it refers to cricket!
The word otherwise is an adverb. It means to do something in a manner that is different.
I cannot think of any way the word 'everywhere' could be used other than as an adverb.
The sentence 'The summer is over' contains 4 words, each of which is a different part of speech. 'The' is the definite article. 'Summer' is a noun. 'Is' is a verb. 'Over' is an adverb.
Game is a noun. It names an activity.
The word over is an adjective
Over would be a preposition in the sentence.
Adjective ( a thrilling game of soccer).
Game is a noun. It names an activity.
Preposition.
The part of speech for tag is verb. It is because when you tag someone in the game, it's an action. But, it can also be a noun as in the game of tag.
Depending on usage, the English language word "game" can be a noun, an adjective, or a verb.
Football (the sport and the ball) is a noun.
What part of speech is this
By repeating the same word over and over again.