"Random" is usually a poorly defined term, so it is impossible to give a clear answer. Many times what is called random behavior in a dynamical system is more appropriately called chaotic. If you plot the output values (however you take them) you notice that certain values are much more common than others, just from one value you can't predict the next. Usually for random numbers the first of many requirements is that all numbers are equally likely.
When you speak of the strength of an encryption algorithm, what you are usually asking is "given certain data (read about cryptology attacks to see what sorts of data are considered), can you learn something about the key or about the plaintext that was encrypted. Encryption algorithms are (should be) carefully designed on this point. Generally speaking you need to scramble the bits in well-defined ways. Dynamical systems are not designed with this in mind and may well have vulnerabilities when used for encryption.