Scrimmage is an interesting and slightly archaic word which, IMO, refers to the point at which two teams come together (as in the scrum in rugby). In American football, it refers to the 'yard-line' at which the two teams line up against each other. Thus a play is successful if the ball is moved across the 'yard-line' and a gain is achieved. Rush has also been mentioned from our song, and this is also still used in American football (eg. he rushed (ran with the ball) for a four yard gain. Total yards is thus split between 'rushing yards' and 'passing yards'. From this, it would be reasonable to assume that 'splendid rush' would refer to running at the opposition with the ball rather splendidly!