Many thanks for the link to your gallery's web page.
I do not have an iPhone X on which to test but I do have an iPod Touch 6 running iOS 12.1.1.
I viewed your gallery in Mobile Safari and let the AutoPlay run through your 39 images.
All images loaded smoothly (without exception) without the spinner ever appearing at all.
I also viewed your gallery (allowing AutoPlay to run through the images) on a desktop browser (Firefox 64.0.2) without the spinner ever appearing there, either.
Just for the record, I am not on particularly good wi-fi at the moment (10.95 Mbps download speed going through a wi-fi extender).
I realise that the iPhone X is more modern and powerful than my iPod Touch and that your wi-fi is probably much better than I currently have but the results of my tests seem to suggest that the gallery on your web server is fine.
I'm really not sure what the problem could be.
You do not see the problem with any of our demo galleries so this suggests that your iPhone X and internet connection are not at fault.
I do not see the problem with your own gallery (with a lesser device and probably slower wi-fi) so this suggests that the gallery on your web server is fine.
Do you still see the problem with your own gallery on your iPhone X?
It sounds like there may have been a temporary glitch with either your web server or internet connection which has since been resolved.
I can't think of any other cause for the problem at the moment.