1. sth is king = sth is very important, has considerable influence on people
''king' here can be regarded as an adjective!
2. the noun 'king' can be used without an article/determiner in phrases referring to 'king' as a function.
'He was crowned king'. There are many more nouns that can be used like this, all related to functions, positions,, e.g. 'He was appointed executive director' (the verb 'appoint' collocates with names of functions) vs. "I like the Executive Director more than the Finance Director"
3. 'like the king and queen' refers to a particular royal couple.
'like a king and queen' means 'royal-like' (they comport themselves like a king and queen)