What I am still missing is a good analysis of the paper in simpler terms that also checks if AMD‘s comment on this is correct, or not.
Bit hard to say if it's correct or not, as the statement is essentially saying "we're aware of the research done" and that one should just "keep all software up to date and follow normal security procedures." That's giving much away, to read between the lines, but my take on it is that, given the setup of the attack ("...
the attacker has unprivileged native code execution on the target machine and runs on the same logical CPU core as the victim...the attacker can [also] force the execution of the victim’s code") is that the findings are correct, but software fixes for this already exist. Naturally it's in the interest of security to not say too much about what those fixes are.
So - what kind of data can be retrieved by this
Pretty much anything data based, given that the attack is using the routines performed by the Level 1 Data cache predictor to figure out what memory accesses have taken place by a CPU core. The more complex the data pattern though, the harder it is to untangle.
are any of the multiple attack vectors already patched
No announcement appears to have been made, so...yes/no? ASLR attacks aren't new, and the implementation/use of it in operating systems varies quite a bit (Windows kinda uses, Linux definitely does), so it's hard to gauge the response against those attacks. In the case of tracing the memory accesses, AMD may have already fixed that in a microcode release, and just kept quiet about it.
does this work on a current Windows / Linux system
Yes, both.
how easy is it to fall victim if this....?
Doesn't seem to be easy at all, provided one follows normal security procedures - I.e. keep every up-to-date, use appropriate anti-virus software, avoid dodgy websites, don't run with scissors, and never walk under a ladder, holding a black cat, on any Friday 13th.