Official betting refers to wagering on a game that has been declared as such by the governing body of the sport in question. When this occurs, all bets on the market in question will be settled accordingly. This can apply to markets like first goalscorer and match winner. However, it also applies to other markets such as totals and player props.
For example, if you placed a bet on the Stanley Cup outright winners, the results will be determined once all regular season games have been played and the teams have been assigned to their conferences. This means that even if one team pulls out of the championship, bets on their conference winners will still stand. This is different from moneyline bets, where the winner of the game must win outright.
Likewise, the outcomes of Major League Baseball games will be considered official after five innings of play and all wagers on the Over/Under market will have action. This includes overtime and shootout scores. However, if a game is stopped early due to the mercy rule, all bets will be void unless otherwise stated.
For ice hockey, all bets on Over/Under totals will include overtime and shootouts. However, bets on Player props (such as number of goals scored or assists made) will only be graded if the players involved start the game. Multiple bets on correlated events are not accepted, as the sportsbook would be exposed to more risk than they want.