The most important thing: prime the wallpaper first with a good primer, otherwise you'll totally soak up the paint and end up needing three coats instead of one!
Yeah, you can paint directly over textured wallpaper, you don't have to remove it - that's the whole advantage of this wallpaper. But the condition is that the wallpaper still sticks properly and there aren't any spots lifting off. If there are bubbles or loose corners anywhere, you'll need to repair them beforehand with a good wallpaper paste. And the wallpaper should be clean - so just vacuum it quickly or wipe it down with a dry cloth so there's no dust on it.
After that, just prime it! That's really important. A good adhesive primer prevents the paint from soaking into the texture and keeps you from having to paint over it endlessly. I'd go with a high-quality primer, not the cheapest stuff. Then you can do two coats of good paint on top and it'll look great! Textured wallpaper has this nice texture that stays intact and looks more modern than if you smoothed everything out.