I can't find how and if people process VST effects in real time. Is there such a thing where you can load any chain of VST effects? It doesn't make sense to me how such a thing couldn't exist.
Even running in a computer, VST effects are usually capable of running in real time, if by real time you mean 'live' rather than 'offline'. However it is true that most computer platforms introduce a comparatively large amount of latency, which may be unacceptable in some cases.
Is there such a thing where you can load any chain of VST effects?
If you mean a physical device that allows you to load VST effects and typically run them with less latency than a general-purpose computer - yes, such things do exist. Examples are the Muse Receptor and Seelake Audiostation.
Note that even these - and all digital effects - will introduce some latency when placed in an analogue signal chain, due to the A/D and D/A processes. So depending on how much latency is acceptable to you, you might consider that no digital effects are truly 'real-time' in the sense of being latency-free.