Is this grammatically correct? omitting "and"

As Greybeard says, in your sentence people are posting the cultural sites and monuments online. They're not. They are posting clips, films or movie clips. You need to rearrange it.

I think this would be the most precise way to say it:

It is terrifying to see, posted online, recordings people have made of themselves demolishing cultural sites and monuments.

Or possibly:

It is terrifying to see recordings people have made of themselves demolishing cultural sites and monuments being posted online.