How to convince the employer that I am the one for the job?

Applied for this job - Administration Officer - (for a Recruitment firm) Job duties:

Our Singapore team is experiencing an exciting expansion plan and requires a professional with the ability and hunger to cover the following tasks

Coordinating reports

Monitoring key performance indicators

Assisting with financial projects

General administration duties

Internal recruitment /involvement in business expansion

Handling PR projects/ social activities

Requirements -

Hands on and able to hit deadlines

Proactive individual who gets things done

Enjoys being creative and suggesting new ideas to improve business processes

Energetic and "can do" approach to work

I went for the interview and after a few days, I wrote to them to follow up and was told - "we have decided not to take things further with you for this position". Then I went to take a look at their website and noted this - the same position (same job description) but title different - OFFICE MANAGER/PR MARKETING MANAGER

What can I do/write to make them reconsider me for this job?

Their expansion plans fit in very well for me. The manager said that later I could move in HR/PR/Acounts etc. I told him that I had an interest in recruitment but the only area that I could not do was PR. However, I clarified what type of PR work (no need to speak to Media) was required, I told him that it would be no problem.

Age group that I would be working with - younger than me. I said no problem.

What to do? I really interested in working for them and growing with this company. Any suggestions? Can I ask him to re-consider? What should I write?