Applying for a job at a company where I didn't get a different position before

All, any thoughts on this sitch would be much appreciated.

I’ve noticed a position at a company (we’ll call it Company X) that I believe I’m uniquely qualified for. It’s similar work to what I’ve been doing for the last eight years. What’s more, my last job did well-received work for Company X five years ago, and I was lead on that project.

However:

  • I had an interview with Company X about 18 months ago - for a different position - and did not get the job. I have some guesses as to why, but I don’t know anything for certain.
  • A former co-worker of mine arranged for the interview.
  • However, by the time I got to the interview, this former co-worker had left Company X. I didn’t ask, and they didn’t say, why, but it appears that he did not leave on good terms.
  • I was still working at my last job at the time of the last interview. In June of this year, I was laid off.

So… when I go about applying for this position, do I refer to the fact that I had interviewed at Company X before? In which case, do I mention experiences I have had since then that would make me better qualified, or that I’m a better match for this position than the one I interviewed for last year? Or do I handle this straight, like I’m applying for a new company I read about online?

Any thoughts, and experiences with similar situations, would be very helpful.

Thanks!