In Rubber Bridge scoring, If the player wins two games with the opponent having an intervening game,does the opponent get 300 for their game?
No; the 300 point "game bonus" does not exist in Rubber Bridge. It is a creation of the Duplicate game in order to properly reflect the value of a game. See Rubber Bridge Scoring for an example that includes a fully scored 2 games to 1 rubber.
While correct, the answer by Joe misses a possibly important subtlety: there are more than just two scoring tables of interest here. In addition to the pure Rubber Bridge Scoring Table, many casual players use the Chicago, or Four-Deal, Scoring Table. I suspect the question may arise from a conflation between Rubber and Chicago scoring.
In pure Rubber bridge Scoring, no Game Bonuses are awarded. (Exception: At the conclusion of the session and before settling, if just one side is vulnerable in an uncompleted rubber they are awarded 300 Points.)
In Chicago or Four-Deal scoring, a (pseudo-)rubber is completed every four hands. The vulnerability on the four hands is, depending on variant, one of:
2nd: Dealer's side
3rd: Dealer's side
2nd: Non-Dealer's side
3rd: Non-Dealer's side
In both variants a Game Bonus of 300 Not Vulnerable or 500 Vulnerable is awarded for bidding and making Game on any of the 4 hands. Additionally, there are variants where Part Scores are carried over within each Four-Deal (pseudo-)Rubber; but that gets beyond the scope of this question and may have further sub-variants.
So before giving a definitive answer to your question: What Scoring Table was in agreed use? Was it the pure Rubber Bridge Scoring Table? Or was it one of the Four-Deal/Chicago Scoring Tables? The meaning of "Vulnerable", as well as the significance of the intervening bid-and-made Game by Opponents, depends on the answer to those two questions.
Here is the theory of scoring (as I understand it).
If you win a "rubber," 2 games to 0, you get a 700 point bonus. If you win 2 games to 1, you get a 500 point bonus. The average of these is 600 points. In this instance, by winning one game, the opponents have reduced their loss from -700 to -500, an improvement of 200 points.
So what happens if play is interrupted after one game? Half of your theoretical 600 point bonus for two games is 300 points. That's where the "300 point" rule comes in.