The game of Sevens! Who said what?

Haskell, 151 bytes

s n|elem '7'(show n)||mod n 7==0=(0-)|0<1=id
a=scanl1(+)$map($1)$scanl(.)id$map s[1..]
f m n=mapM_ print[[x+1|x<-[0..m-1],mod(a!!x-1)n==i]|i<-[0..n-1]]

*Main> f 30 5
[1,6,8,13,15,19,23,30]
[2,7,12,16,18,24]
[3,11,17,25]
[4,10,21,26,28]
[5,9,14,20,22,27,29]

Pyth, 38 bytes

Jm[)EA,01VQa@JZ=hG=+Z=W|}\7`G!%G7H_H;J

Try it online. Test suite.

Basically a port of my Python answer; there's probably a better way. Takes as input the number to count up to n and the number of players p on separate lines, outputs the result as a two-dimensional array.

Python 3, 155 bytes

from turtle import*
def f(m,n,i=0,r=20,d=360):
 k=n
 while i<m:i+=1;fd(r);write(i);bk(r);e='7'[:i%7]in str(i);d*=1-2*e;k=~-e*(1-k)%n;r+=(k<1)*15;rt(d/n)

Uses turtle graphics to print in a circle such that numbers spoken by the same player are on the same radius. The radius of the circle is increased when the direction is reversed, or when the sequence wraps around the circle, so previous numbers aren't overwritten.

Sample output for f(22,6)