Here are DigitalZoomStudio we strive to make our products as optimised as possible.
Video items are custom wordpress posts.
It’s just like having 1000 normal blog posts. There are many wordpress sites with even hundred of thousands of posts which have no issue with performance so nothing to worry about.
If you feel performance is suffering or you need faster server speeds , you can
Install caching plugin like w3 total cache
Upgrade your hosting
The only time performance can suffer is when you add 1000 items in the same gallery . When this is rendered on the client side, it might cause the client machine to suffer a bit by rendering them at once. So maybe distribute those items via separate playlists, or use pagination.