To pass match data to your game server, serialize request.MatchmakingResults in your Cloud Code allocator and include it as a payload when you request the server from your hosting provider. This gives the server the full match context: player list, match ID, properties and per-player custom data.
This applies to Matchmaker pools set to Hosting via Cloud Code.
var payload = JsonConvert.SerializeObject(request.MatchmakingResults); // Amazon GameLift: set GameSessionData = payload // Other providers: check your provider's session creation API for the custom data field
The field name for the payload varies by provider.