Can business projectors show video?

This simple answer is a qualified yet. The vast majority of projectors support video as well as data, you'd have to look hard for one that doesn't. The qualifies bit is more about quality then whether it can or can't. Most business projectors are optimized - both in their signal processing and brightness - for giving business presentations possibly in relatively high ambient light. This means that they will generally be too bright for home cinema use with controlled lighting. For a list of machines that may be suitable to you for both purposes see out home cinema list under "Projectors" and scroll to the second list "High Definition Ready Presentation Projectors".