When used in this way, it usually means that the player concerned has not chosen the best option available, and is perhaps thinking more about individual prestige than team success. The types of goals that make the news headlines are usually something special. They are typically ones scored against all odds: a player shoots from 40 yards out; a player dribbles from their own half, beating several defenders and chipping the ball over the keeper's head; a player scores with an overhead scissor kick in the final seconds of a game. These are the goals that bring glory, and kudos from fans and team mates.
However, a player 'going for glory' may overlook a much better scoring option, such as an unmarked team mate waiting in the 18-yard box, or a steady build up of play following a team plan.
As a prominent example, Cristiano Ronaldo was heavily criticised in some circles in Portugal's semi-final loss to Spain during the Euro 2012 tournament. Ronaldo was accused of wanting to take the glory penalty (the final penalty, after which everyone celebrates and holds the victors high - assuming it all goes to plan), rather than taking an earlier attempt, which may have kept Portugal in the hunt for victory.
In a similar vein, a player who misses a fairly routine goal opportunity can be said to have been "too busy reading tomorrow's headlines", meaning that they were not focussing on the task at hand, and preempting the celebration of scoring.