You have that most probably from a chess book.
Auf Gewinn stehen means you have (reached) a position which should be winning. "He was winning" or "he had a winning position" is an adequate translation. The reason why "stehen" (standing) is used in German is because a "position" is called a "Stellung" and this noun is related to "stehen".
"Zeitnot" (time trouble) is a word that (in German) made it from chess into everyday language, similar to "Zugzwang" (which even made it to English) or "Hängepartie" (adjourned game).
In tournament chess one has only a certain amount of time (a common time control for tournament games would be 2 hours for the first 40 moves, 1 hour added for the next 20 moves and 30 minutes added for the rest of the game, blitz is much faster, commonly 5 minuted for the whole game, nowadays often 3min for the game with 2 seconds added for each move made. Time is measured with two connected clocks. At the beginning of the game whites clock begin to tick down, then after he makes a move he presses a lever which stops his clock and sets the one for black in motion - and so on. When the respective time of a player is over the opponent wins, regardless of the position.
Therefore, a player who has only 5 minutes of the respective allotted time left is considered to be in "Zeitnot" (time trouble). It is expected that he will have problems because he is forced to make moves on instinct without having considered them properly.
Some players - even top players - tend to get in time trouble quite regularly: Aleander Grischuk, for instance, is famous for most times having only a few minutes left at move 20 or so and then blitzing the rest of the game. It hasn't prevented him from being one of the best players in the world.