Now that you have added the photo my advice is to buy the adaptor listed on the label. If you search for 'NES-200E' you can buy one with the exact specs required.
I will leave the advice below as record and as general advice for people looking for power adaptors.
I am not an expert in this area but I have some working knowledge and use to work in a store which sold generic power adaptors.
Generally the answer is yes, the additional 0.3A is important.
The 9V, 1A adaptor is rated to supply up to 9W (Watts) of power. Assuming that the information in your question is correct the SNES requires up to 11.7W of power (P = V x A) this means that the adaptor is only capable of supplying the SNES with about 75% of it's potential maximum power requirements.
If you are looking for a power supply then it needs to match the voltage (9V) and be able to provide at least the required current (1.3A). It can be rated to a higher current as most power adaptors are 'regulated' which means that the power supply will allow the device to draw the current it needs (up to the maximum rating) at a constant voltage.
My advice would be to buy a power adaptor that is specifically for the SNES rather than a generic one and if this one is suppose to be for the SNES then I would be very cautious about it, especially if it is non-branded from e-bay. This has the potential to damage the console beyond repair and be a fire hazard so it is definitely worth paying a few extra dollars and getting a known brand.
It is possible that the 9V, 1A power supply will be fine as the SNES may never actually try to use the more than 1A but it is pretty difficult to know that for sure. If other people are using the 1A power supplies without issues then they may be OK but keep in mind that, typically, consumer electronics are not over specified and it's likely that the original power supply was rated to 1.3A because that was what the the SNES required.