How do point mutations arise from mistakes in DNA replication?
Source of your misunderstanding

Your misunderstanding is very comprehensible as the figure is misleading.

The figure only shows a single event of replication. What you see as a second replication resulting into two double stranded molecules is NOT an event of replication. It actually represents the two possible outcomes from a 'mismatch repair mechanism'. The term DNA replication written on the figure should be replaced by Possible outcomes of DNA repair. The molecule that contains the G-T mismatch is therefore just a temporary state that will very quickly be changed to either the T-A state (bottom right of your figure) or to the G-C state (upper right of your figure). More information below.

DNA repair


  DNA repair is a collection of processes by which a cell identifies and corrects damage to the DNA molecules that encode its genome.


The type of DNA repair that is of interest on the figure is called "DNA mismatch repair"

DNA mismatch repair


  DNA mismatch repair is a system for recognizing and repairing erroneous insertion, deletion, and mis-incorporation of bases that can arise during DNA replication and recombination, as well as repairing some forms of DNA damage.


There are specific enzymes to repair a mismatch such as the G-T mismatch represented on your figure. These enzymes can either repair G-T into G-C or into A-T. If the repair is A-T (lower outcome in the figure) then a mutation would have occurred. If the repair is G-C (upper outcome in the figure) then we are back to the original sequence and no mutation would have occurred.

Note that the probability of the two possible outcomes is different from 0.5 as these enzymes have ways to try to figure out which was the original strand and which was the newly replicated strand. You can learn much more about the mechanism of DNA mismatch repair on the wikipedia > DNA mismatch repair.