xomm :
The first number denotes the generation. The second and third numbers denote the tier.
Cards of the same tier ascend in power by generation (i.e. 7970 > 6970)
Cards of the same generation ascend in power by tier (i.e. 7870 > 7770)
If a game requires a 9600-series card (which won't come out till the end of the year), it likely isn't too demanding (cards marked X6X0 tend to be re-releases of old cards.) A relatively powerful 3000-series card like the 3870 could probably outperform it due to the difference in memory bandwidth, despite the 6-7ish year gap.
There is no way that a game would require a card that not only hasn't been released yet, but hasn't even been confirmed yet. BigMac is right in that it must be an older game requiring the ATI 9600 series, not the (not yet been released) AMD HD9600 series.
On top of that graphics performance roughly has doubled every 2 generations of graphics cards (getting closer to doubling every generation now). There is no way the HD3870 will out perform something in the 9600 series. This is clearly shown in the link that k1114 posted since the HD3870 is shown to be lower tiered than the HD5670 and the HD6670 (the HD7670 is only an OEM card right now and not ranked, but would be higher than the HD3870 as well) Which clearly means that any HD9600 card would also be higher than the HD3870.