There are four teams.
1 - Some games, like golf, would be played once.
2 - Each team would play against one other team. There is a case to be made that this is unfair.
6 - Each team would play each of the the other three teams once, which works out to six encounters.
+1 - Championship between the two best teams from previous ecounters.
 
 
 
 

Alpha
+++++
bowling
fussball 2 played against the soccer team you play against
indoor soccer 2 + 1
Go 2 + 1
trivia
treasure hunt!
 
 

FUN IN THE SUN
++++++++++++++
first two encounters of a surprise volleyball tournament
Trivia and Boggle word game
Konane 6+1
tennis, golf
 
 

CABIN FEVER
+++++++++++
bowling
Trivia and Boggle word game
King of the Mountain, Tablut, Snowflakes memory game, crokinole
curling, hockey
surprise snowshoe race?
polar bear dip surprise challenge, although I'm not sure where.
 
 

FRIDAY NIGHT
++++++++++++
bowling
dudo a.k.a. Perudo surprise challenge
could throw in karaoke for low points as part of something else
darts 2, pool 2, fussball 2
movie trivia, word game like game show
ping pong
poker - high stakes! Villa Paletti balance game, a bit of backgammon?
more bowling
 
 

BISON
+++++
bowling
Could have tinikling for no points as an early icebreaker. Amazing Race did a variation of this, I believe in Taiwan.
trivia, Manitoba birds identification
The Oak Games: Snaps, Sand Dollar, King of the Mountain
treasure hunt!
dragon boat race
For the symbolic trophy, I would like to see some bark biting.
 
 

Special Forces
++++++++++++++
bowling
trivia, maybe some decoding.
chess (or - surprise! - it's actually a chess variant)
archery
military training style challenge, obstacle course. Who will wash out?
paintball, preferably outdoor
a blind sport
 
 
 
 

These scenarios are light on surprise challenges. They nicely belong in the treasure hunts.
 
 
 
 

Abstract strategy games pool:
African games! Yote, Fanorona and mancala
Go
Camelot