Well, to sound 'game-like', it should fit the context and the intended era; so long as it doesn't sound outlandishly unfitting it's fine IMO. So if you wanted to write something Final Fantasy Tactics-like, something like the Roland SC-88 could give that type of atmosphere, and then you would just need to write something to fit the context given for the game.
Central Bark specifically sounds like a track with a smooth jazz feel (brush snare, e. piano, guitar, pluck arp, synth bass) and a slight chiptune influence to make it somewhat more game-like (but it wasn't necessary, assuming Central Bark is supposed to be like a stroll through a park, which was apparently the goal anyhow, now that I look at it).
The first track does lean much more towards chiptune though. It sounds like a mixdown with a C64 arp, an E. Piano, vibraphone, and probably Roland TR-808/909 drums.