The red spot was supposed to be blood. The plot of the play had Landon's character get shot in the arm prior to the scene for some unrevealed reason (we can assume that it has to do with his alcohol running). If you look closely you will see that he barely moves that arm the entire scene because it is supposed to be injured. There is not much blood because this is a PG rated movie.
In the script, Landon's character was supposed to be mortally wounded and making a deathbed confession to God when Alicia (Jamie) walked in.