Is a cut glass edge not sharp? It was hard to watch him run his finger along the edge like that.
So yeah, I don't recommend the practice if you're not sure, but it may be okay for glass that has had edgework done as this glass gets polished smooth, whereas tempered glass is probably okay, but not always safe.
EDIT: Looks like it's blown glass. No, that's not very safe.
This is not surprising, since it's basically like cutting it with 60-180 grit sandpaper
Those really suck.