You really need to find the resolution that the synthetic spectra were generated at. This isn't something you should be trying to find from the spectra themselves.
From the Table you have shown, you appear to have just divided the wavelength by the bin size to get 330,000 for the resolving power. (NB Resolving power is the wavelength divided by the FWHM of a resolution element. The resolution is the FWHM of the resolution element.)
It is highly unlikely that this gives the right result because then your synthetic spectra would be undersampled.
However, if you can assume that the line broadening in the spectra is dominated by the imposed resolution of the spectra, rather than the intrinsic broadening of the lines and turbulence present in the atmosphere itself - which might be true for relatively low resolution spectra - then a possible procedure is to take the Fourier transform.
The FT will be that of the convolution of random delta functions with the line spread function. The result will be the product of the FT of the random delta functions and that of a Gaussian (which is also a Gaussian). This should give you a total product that has a Gaussian envelope. The inverse of the frequency-space width of this Gaussian envelope should then be an estimate of the Gaussian sigma corresponding to your resolution.
Perhaps an easier rough way of doing this is to try and find what look like isolated absorption lines and fit them with Gaussian functions. The FWHM of those Gaussians is approximately your resolution (it is actually an upper limit, because it assumes the intrinsic broadening is negligible).
A final thought is that perhaps the resolution is limited by the number density of pixels in the synthetic spectra. In which case, it is possible that the spectra have been binned to have a resolution (FWHM) of 2 pixels? But from the information you have given I suspect that the resolution element is more like 10 pixels.