I understood the sentence below:
この面白い話を落語と言い、落語をする人を落語家といいます。
as to be:
Such interesting stories are known as 落語, and people who tell 落語 are called 落語家.
However, if the meaning is as I have interpreted, what is the grammatical rules with regards to the usage of を in the above? Would it also work if it was simply
この面白い話「が」落語と言い、落語をする人「が」落語家といいます。
Sentence lifted from Lesson 20 of Genki II.
Using を when not followed by a verb
But 「言{い}い」 and 「いいます」 are both verbs in:
「この面白{おもしろ}い話{はなし}を落語{らくご}と言い、落語{らくご}をする人{ひと}を落語家{らくごか}といいます。」
「言い」 is the continuative form and 「いいます」 is the masu-form of the verb 「言う」, isn't it?
Thus, 「言い」 is used mid-sentence because the sentence still continues after it.
「Noun + を」 does not need to be followed directly by a verb. There can be other words placed in between as in:
「ラーメンをおいしく食{た}べる」
「カーテンをゆっくり開{あ}ける」, etc.
Hope you are following this explanation.
「A + を + B + と + 言う」
BTW. is an extremely common set phrase meaning:
"to call A 'B'"
You ask:
Would it also work if it was simply:
「この面白い話「が」落語と言い、落語をする人「が」落語家といいます。」
No, it would not. That would not be natural-sounding under normal circumstances. Careful speakers would not use 「が」 in that sentence.
この面白い話を落語と言い、落語をする人を落語家といいます。
In both parts of this sentence を is followed by a verb. The verb is 言う. There is nothing in Japanese grammar that says the verb must come immediately after を. You've probably heard that word order can be quite flexible in Japanese. This is possible because we know what the part of speech is from the attached particle.
In these two clauses you have the common pattern:
AをBと言う
Call A (as) B.
so your English translation is accurate (I'd be inclined to go with 'funny' rather than 'interesting' for 面白い though).
Finally, you ask if
この面白い話「が」落語と言い、落語をする人「が」落語家といいます。
would be correct. The answer is no. が marks the subject of the verb 言う. The subject would be the person doing the calling、i.e. the person making the claim that these funny stories are called Rakugo. In your original sentence the subject is left unspecified, and we assume it to be just a generic 'we/one/people in general'.
