These children's favorite indoor game is chess- what is the subject here

As can be read in the comments, some grammarians might consider that there are two subjects in sentences where the verb is a linking verb. Traditional grammar, however, does not allow this possibility.

(Wikipedia) Criteria for identifying subjects

There are several criteria for identifying subjects:

1. Subject-verb agreement: The subject agrees with the finite verb in person and number, e.g. I am vs. *I is.
2. Position occupied: The subject typically immediately precedes the finite verb in declarative clauses in English, e.g. Tom laughs.
3. Semantic role: A typical subject in the active voice is an agent or theme, i.e. it performs the action expressed by the verb or when it is a theme, it receives a property assigned to it by the predicate.

In the sentence in question, the predicate "is chess" assigns a property to "These children's favorite indoor game".

Of course, the sentence implies that chess is these children's favourite indoor game, and so, it could be argued that "chess" is also a subject, but what is being talked about in the initial sentence is not chess, what is being considered as central in the utterance is "these children's favorite indoor game". The property of being chess is not received by "chess".

(wikipedia) Technical definition

The subject […] is, according to a tradition that can be traced back to Aristotle (and that is associated with phrase structure grammars), one of the two main constituents of a clause, the other constituent being the predicate, whereby the predicate says something about the subject.

These children's favorite indoor game is chess.

The subject is "these children's favorite indoor game", and the predicate is the verb phrase "is chess"

The copular verb "be" has the noun phrase "chess" as subject complement, so-called because it refers to the subject. In your example, the complement defines the childrens' favorite game as being chess.

The structure is thus S-V-C.