the first is where and when and the second is theme
This is an 'adverb infinitive'. It is not a participle, either present of past, because it doesn't end in -ing. And it is not an 'adjective infinitive' since its meaning is adverbial, 'you must capture or trap the other king' IN ORDER 'to win a game of chess'. Adjective has to modify a noun, which isn't the case in this sentence.
The correct answer is unselfish
1 would be word divided in syllables
2 is word with double consonants
3 is a hyphenated number word
4 is hyphenated adjective
5 is two word compound
6 is hyphenated compound
7 is one word compound