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There are total $\frac{2024*3}{2}$ wins, so we can not have more than $\frac{2024*3}{4}=1518$ happy players. And it is possible. Give every player a number from $1$ to $2024$. Then let $1$ won against $2$, $2$ won against $3$,... $1517$ won against $1518$, $1518$ won against $1$. Now let $1,2,3$ won against $1519$, $4,5,6$ won against $1520$,..., $1516,1517,1518$ won against $2024$ Easy to see, that every player from $1$ to $1518$ has two wins and is happy, and from $1519$ to $2024$ has zero wins