I don't get paid to play and I have no contract to play for him, so if I was "running" his team then that makes me an employee???? So should I not be paid wages for my work??
This need not be the case if running a team for someone it does not mean you are employed, and if considered work it can be voluntary work. And as you say: no contract, so if thats the case then certainly no employment contract.
I know nothing of the team or the circumstances but there are probably quite a few things being said here that should not be in public.
In generalised terms there is no requirement for a contract to be written to enable it to be valid, it makes it easier if it is documented.
The key points are offer, acceptance and consideration. But also an intention for a contract to exist. If one party feels there is a contract the other may not.
In the specifics of this there may be a contract in place which you inherited by becoming a member of the team, and then took on more responsibility to the contract by becoming co-captain.
Even though the new season had not started, it would not mean the owner/sponsor isn't going to expense in preparation
How this affects your circumstances depend on the details