The authors acknowledge that there are equal numbers of negative and positive items in the Oxford Scale, but happiness can be indicated by not agreeing with the negative items.
As Kashdan (2004) explains it in the following paper, that scale is not a good measure of happiness. For example, it's items measure variables such as extraversion that are related to happiness.
Kashdan, T. B. (2004). The assessment of subjective well-being (Issues raised by the Oxford Happiness Questionnaire). Personality and Individual Differences, 36, 1225–1232.