OFDM Times of Arrival of multipath
I don't fully understand your question, since you correctly state


  $\tau_i$ are delays of the multipath


therefore, $\tau_1$ is simply the delay incurred by the shortest path.

And no, $\tau_{i\ge2}$ are not relative delays; look at the formula: you just add up different independent paths with different delays; every path has its own delay, which is totally independent from $\tau_1$.