35.Q(27,20)+
Four-Player Infinite Chess - The Battle of Morgarten!
What happens if one person makes a discovered attack against an enemy's king, but with his team-mate's piece being the one uncovered? So on the teammate's turn, he can just take the king?

Horus, I believe in that case it would be checkmate, if his teammate could not intervene in time.
"Hours"

What happens if one person makes a discovered attack against an enemy's king, but with his team-mate's piece being the one uncovered? So on the teammate's turn, he can just take the king?
I'll try to play my move tomorrow, but for now I think this explains situation to HorusTheThird's question:
I believe hitthepin is right, except with the clarification that if two kings are standing, the king can be captured. Here's a description (players A, B, C, and D):
Scenario #1
Team-1: (AC)
Team-2: (BD)(assume both kings standing)
A moves so "C" has discovered check on "D"
B Must parry the check if possible to do so.
C If B is unable to parry the check, then C can capture the D king.
(One of two kings is gone)
D ...
Scenario #2
Team-1: (AC)
Team-2: (BD)(One king standing)
A moves so "C" has discovered check on "D"
B Must parry the check if possible to do so.
If B is unable to parry the check then Team-1 checkmates "D".Team-1 wins!
(hope this makes sense)

In 4-player chess, the rules are simply to allow king capture. And a captured king results in the same as checkmate.

But isn't 4-player chess four individual players? I think that's one of the differences here: It's really like two teams against each other. Each team has two players. I like the system of teams working together, but it creates nuances where making specific rules can be a little more complicated.

One example in 4-player chess (first posted by @e4bc4qh5qf7)
The answer is written below:
1. | Nf12 | j6 | Bg11 | d10=Q+ |
2. | Ne10+ | f6=Q+ | Bxd14 |
And since the game is over with the first checkmate/king capture there red and yellow wins.

But isn't 4-player chess four individual players? I think that's one of the differences here: It's really like two teams against each other. Each team has two players. I like the system of teams working together, but it creates nuances where making specific rules can be a little more complicated.
4-player chess has 2 variants. Teams and free for all. But king captures are possible in both through discovered checks.
Sorry for late reply, especially considering my move was forced:
33.Q(18,20)+...C(8,10)
34.Qx(20,8)+...K(16,9)