Originally, Bitcoin had a value of zero. But then, a while back someone bought 2 pizzas for 10,000 BTC. This put the value of 2 pizzas into the overall system. It was a tiny amount but it still counted. Others have bought drugs and other contraband with BTC. Some have exchanged work for BTC. Some people bought electronics. All of these tiny amounts add up until a currency that is worth essentially zero begins to have value. A while back, a single BTC only traded for a penny but the "intrinsic" value was in there and it grew.
You are misunderstanding what intrinsic value is. You're talking about market value. There is no intrinsic value to bitcoin, only market value. Intrinsic value is typically calculated in finance by looking at the sum of the future income that's generated by that asset, in terms of discounted present value.
What you describe in your post is entirely about market value, which is the only value an unbacked currency has.