Is there a lot of dialect in this text related to Japanese, I can't find out how to look it up.

This is an article about Japanese "comic" rakugo. Some of the words/sentences listed in this article are not so much "dialects" as they are classical "jargon" or early folk slang, and are not the same thing as "dialects". The so-called "dialect" is not the same concept. Because the Rakugo language itself originated in Edo (i.e., present-day Tokyo), its speech and terminology are basically "Edo" or "Tokyo". And the modern standard broadcasting language of Japan (equivalent to what we call 'Mandarin') is 'Tōkyō'. Therefore, the "Rakugo" language introduced in the article is not a dialect. It is just a special kind of "jargon". Just as some of the words used in our "comic dialogues" do not appear in the standard published "dictionaries".

Combined with the classic paragraph "Three Parties, One Tael Loss", in which the character's words are in the "Edo language" of the past 100 years