What piece is on 8c?
Chu Shogi Puzzle #1

8c is an eagle, so Gote's king is attacked. I remember taking over 2 days to play DK-8c+ (from 8l; not a capture either).

The only moves to consider are K - 5a and K - 7a
Right. One leads to the king getting forcibly captured. The other continues further. Would you prefer that I reveal the first move response to either choice, or do you prefer to solve it by yourself?

Actually, K-7a is met with DH-1g, and there is no stopping that. K-5a is followed up by SE-6c. If we follow your idea, K-5a Ln-6c DKx6c SEx6c Ph-5d seems simplest - no mate.
K-7a DH-1g (offering the lion for king) Ln-7d (offering the lion to stop mate) DKx5b (with discovered check, refusing the lion) DK-6b DKx6b Lnx6b DHx6b+ Phx6b Ln-5c mate
K-7a (with best defense, mate in 25...) DH-1g Ph-6b DKx6b BTx6b DHx6b+ DKx6b SE-5c K-7b SEx!6b BT-7c B-4f K-8b Ln-6c K-9b Lnx7c K-10a Lnx8a K-11b SE-6b K-11c B-9a+ K-10d Ln-8c K-11c Ln-9b mate [Epic king chase variation]
What game is this
It's called chu shogi, which is a variant of shogi (the Japanese version of chess).

The rules can be found here https://en.wikipedia.org/wiki/Chu_shogi
You have the best chance of finding live opponents here: http://81dojo.com/client144.html
Occasionally people play here: https://sdin.jp/en/browser/board/chushogi/
Or by correspondence on these forums.

I used 龙 instead of 竜 (dragon king) on 5c.
Can you explain the choice to represent the DK this way?That symbol is new to me.

I used 龙 instead of 竜 (dragon king) on 5c.
Can you explain the choice to represent the DK this way?That symbol is new to me.
I wanted to clearly show which pieces are the promoted version with semi-cursive font, so there would be no need to change colour, which could confuse some people. Traditionally, the cursive for 王 was used for promoted version of 竜, but I thought that would be confusing for most people.
The only suitable font I found was for simplified Chinese characters, so I just took the character for dragon, which is 龙. If you look close enough, it could pass for a cursive of 龍, which is the character it was simplified from anyways.
This is a very tricky one. Gote (white) to move. I used 龙 instead of 竜 (dragon king) on 5c. It's almost a mate, but not quite. Defend as best as you can. Puzzle length: 9 moves (17 ply)
Comment 1 move at a time (or with premoves), and I'll respond with another diagram.
A lot of side lines to consider. I've checked over 40 variations, so my solution should be correct.