Almost certainly EMI. You may find ferrite beads, shielding, etc. nearby as well.
So, those signals will have some source impedance (which may be due to the circuits they come from e.g. TTL or CMOS logic, or added impedance e.g. series resistor or ferrite bead), and the capacitor shunts against that at high frequencies, forming a lowpass filter. If the impedance is say ballpark 100 ohms, then 47pF rolls off at ~34MHz. The cable I'm guessing isn't shielded/screened, nor does the connector have a metal shell?, so this helps to reduce radiated emissions (emissions above 30MHz are measured with an antenna, with the equipment in some standard configuration, inside a semi- or anechoic chamber) without having much of any effect on the signals themselves (std def analog video uses under 10MHz bandwidth).
Note that a lower cutoff may have undesirable effects on the video, for example skewing the hue and saturation of composite or S-video. A lower cutoff would give noticeable phase shift and attenuation of the video signal; 34MHz seems high enough to be safe from this. So, we can guess they used about as much as they could get away with here.
As for what they are trying to filter, it's switching noise and harmonics from the CPU and other onboard logic. Though the CPU runs at, whatever, 3.58MHz or a fraction of that (I forget what exactly; also the SPC700 runs faster, doesn't it?), but the switching transitions are what matters, and they are typically fast enough (a few ns) to include significant energy to 100-200MHz. Most of which should be confined to the main board, but due to various limitations (including cheap construction for a mass-market product!), some inevitably gets out along connector boards, cables, etc. So additional shielding and filtering tends to be necessary.
The same is true of the controller ports, which are also unshielded cable (AFAIK). I don't have an SNES, but I recall my NES controllers actually use a CD4000 series shift register on board, with no bypass capacitor on that long cable! CD4000 at 5V, is very slow, evidently slow enough to get away with this -- and a similar interface on the mainboard can keep EMI low, allowing emissions to pass.
A similar mechanism is used to this day, on USB HMI -- keyboard, mouse, etc. typically have unshielded cables, using a particularly slow communication mode that is tolerant of noise and less prone to emission. Or, for USB Full Speed (12Mbps), limitations are very similar to the video signals above (but without analog levels!), so it can be filtered in a similar way (though this is less useful, as USB is still quite sensitive to common mode interference, and is almost always carried on shielded cables and connectors).
Tim