The data points are not rendered when the series' axis is set at runtime through a DataTrigger in the series' style. 

Note: The data points are rendered when the chart is resized or zoomed.

Workaround:
Change the resource type in the DataTrigger that changes the axis - instead of DynamicResource, use StaticResource. 

<telerik:CategoricalSeriesDescriptor.Style>
    <Style TargetType="telerik:LineSeries">
        <Style.Triggers>
            <DataTrigger Binding="{Binding Path=Axis}" Value="Left">
                <Setter Property="VerticalAxis" Value="{StaticResource AxisLeft}"/>
            </DataTrigger>
            <DataTrigger Binding="{Binding Path=Axis}" Value="Right">
                <Setter Property="VerticalAxis" Value="{StaticResource AxisRight}"/>
            </DataTrigger>
        </Style.Triggers>
    </Style>
</telerik:CategoricalSeriesDescriptor.Style>