Does randomness of an event depend on the observer? For example, when a coin is tossed it the outcome may appear random to the person who tossed it, yet to say a supercomputer which had at that time analysed the wind conditions, the gravitational force, angle etc. the outcome would not be random. so in short, can pseudo randomness be equated with randomness if the observer cannot predict the outcome?
To ask "is this random" is a question ambiguous between the two senses of random? Here, we need to distinguish between epistemic (concerned with what we can know) and metaphysical (concerned with what a thing or system in fact is) conditions for randomness.
What you are describing is when we epistemically cannot distinguish between randomness and a complex system which makes an events outcome deterministic (or free) rather than random. In answer to your question as to whether something epistemically random qualifies as random, that would depend greatly on how yo think what we can know relates to reality itself. And it can also depend on the particular case.
So your intuition is right. We might call something random and use it for those purposes even though it is not in fact random on a metaphysical level-- like the random number seed on your computer which depends on jitter in electronic magnetic pulses or on background radiation. But then do we ever care that the thing is metaphysically random rather than random to our knowledge.
Can pseudo randomness be equated with randomness if the observer cannot predict the outcome? No. Consider this thought experiment. You and I are playing a card game. As far as you know, the deck is fairly shuffled, so the sequence of cards is random. But in fact, I stacked the deck, so it appears random to you, but the sequence is entirely known to me. Clearly, I have a strong advantage in the game.
In other words, just because the observer can't tell the difference, it does not mean the impact is the same. Even in the case that no other conscious observer knows the pattern, the fact that there is a pattern could alter the results in a way that might be significant. This is a problem with practical implications. (See this article for how this impacts cryptography, as an example.)
This is especially significant given that it's unclear whether true randomness exists in the universe, or whether what we experience as randomness is just patterns we don't as yet understand.