hi christiano~
I have looked at the site you linked.
yes it can be done with Hype.
looks like they used javascript to have random effect.
I think there will be another person to help you out with coding.
if you know how to code then you can simply ‘pause timeline’ action on each photo and put ‘run javascript’ action.
or if you like to go without coding you can edit the photos with photoshop and make them move like the effect.
I think making the effect to look like the site you linked is not easy to make without coding.
hope my answer helped you.