Its because they re-enter from orbital velocity.
The max speed reached by the Virgin thrill ride is about 2600 mph, by contrast a spacecraft in low Earth orbit is doing close to 16,000 mph.
That speed has to be dumped somehow. There are two ways to do this, powered decent, or aerobraking. Powered decent was used on the Moon because, obviously, there's no atmosphere and the low gravity makes it feasible ( Lunar orbital speed @ 2200 mph). Less speed to dump.
OK, so in order to *be* in orbit around the Earth you must be doing around 16,000 mph. Carrying enough fuel up to do a powered decent is unrealistic, so both the Virgin craft and (for example) the Space Shuttle, use aerobraking.
The difference is the shuttle needs to dump a *lot* more speed. Speed = energy = heat, hence all of the heat shielding.
The Virgin ride is, actually, kind of poor value compared to that $20m Soyuz flight if you take into account the amount of space-time you get per dollar. $200,000 buys you 6 mins, Mark Shuttleworh coughed up 100 times that, but got 11 *days* of flight time.