Passmark is beyond inaccurate (it's a synthetic and is thus only good for comparing nearly identical models) and the Tom's article clearly shows how the Phenom II x4s are right with the i3s. That chart doesn't take BF3 MP nor some new games into account (the i3 wouldn't have a chance in those), so it's also a little inaccurate, but even without that, they're pretty darned close on average. Also, most modern software outside of gaming is able to use four or more threads quite well. So, yes, your view is dated.
The 5800K, as a CPU, is faster than the Phenom II x4s (also, an 810 has a very low frequency and less cache than the 9xx models, so it's irrelevant even if Passmark was accurate) as a result of its similar performance per Hz to Phenom II and its high frequency. It'd be in the same bracket as the i3s.
As proof of how bad the 810 is, here:
http://www.cpubenchmark.net/cpu.php?cpu=AMD+Phenom+II+X...
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i3-2...
The Phenom II has a roughly 10% advantage over the i3 in this example of Passmark.
I'd get a 7770 and an A10 in this situation.