[Casiopea]

1. Worse, Japan's game makers underestimated the importance of creating games for a maturing audience. --here, “maturing audience” means the players who are growing up, and maybe their taste are changing gradually, or simply means the adult players.

mature audience means, an audience that has matured; they are mature.
maturing audience means, an audience that is in the process of maturing; e.g., ". . . for an audience that's growing up, getting older and wiser."

2. While most Japanese developers continued to create impressionistic, family-friendly fare, rivals offer plenty of blood, bullets, guts, and gore to satisfy the gunslinger in every game player.

“impressionistic, adjectival form of impressionsim
“fare”, range of products
“guts”, entrails
“gore”, blood shed

3. . . . the Japanese have largely kept their resources at home, coming up with offbeat products . . . ,

“offbeat”, eccentric, unconventional.

(1) bankable franchises

bankable sequels

(2) Final Fantasy franchise

Final Fantasy sequel

(3) franchise characters

sequel characters
The sequels will sell because the first X in the series was profitable. A franchise is a business that is authorized to sell the products of another company; e.g., McDonald's. The business does well because McDonald's did/does well.

5. Soi 33 on Sukhumvit Road, Bangkok, has long been an expatriates hang out.

An 'expatriate' is a person living abroad; renounces their citizenship. 'hang out' is a place where people go to let it all 'hang out', to relax, to let loose. Cf. A tourist is considered to be a foreigner.

6. The theme here is usually that of a hostess bar, some have waiters, Christie's has doormen in bizarre uniforms! You will be ushered in and given either a hot or cold towel. The first bar here was Renoir, then followed Christie's, Napoleon, Van Gogh, Degas, Manet (now Monet due to a sign writing error!) Leo Club (now Santana), then a few more appeared. Recently, in 2004 the "painter" theme has been continued with Gauguin.

A “hostess bar” is a club where women work as hostesses. Their job is to "chat" with male customers. In Asian society - more so in the past - marriage was considered a business; people usually did not marry for love, so a married couple had little or nothing in common. 'hostess clubs' filled a need for many men - married and single. There aren't any host bars.

how do the first two sentences relate to the rest part of this paragraph?

What is your best guess? Consider this, in the first sentence 'theme' is used and in the last sentence "painter theme" is used.

7. …These are mostly hostess bars, and offer a more refined and laid back ambiance. The girls are basically the same as those you find in other [hostess-like establishments], just enjoy the illusion, [they aren't as naive as you think they are, but] they play the part quite well. Most, if not all, have danced round a chromium plated pole at some time, and may well do again in the future!

Before becoming 'hostesses', the girls were dancers; i.e., probably strippers and/or prostitutes, and they'd probably do it again because it's (a) what they know and (b) pays more than an office job - if they have the schooling and experience to get an office job.

Take a look at the parts I added in, [ . . . ].