Hi Tschimm, sorry about the slow reply!
It's actually written correctly, but I can see why it's confusing.
You're right that E contains E G# B, but C#m7 contains C# E G# B, i.e. the same notes as an E chord, plus C#. It's very common to leave some notes out of chords, and in this case Frusciante has chosen to leave out the C#. If you do this, it's exactly the same notes as an E chord, so how can you tell which one it's meant to be?
Sometimes it can be really ambiguous, and it's hard to come up with a definitive answer about which chord name is more suitable. In this case, I'd say there are a couple of strong clues about which name is better. Firstly, the bass is playing a C# root note in that spot, which means it's functioning as C#m7 rather than E. Secondly, he's playing a straight C#m in that spot elsewhere during the verse, so the chord in question is extending that C#m chord into C#m7 rather than replacing it with E.
Hope that helps!