I find it interesting that Jakob's solution worked. I think that actually shows a bug Unmarshal: a json.Number is supposed to represent a JSON numeric literal, but here we see it decoding a JSON string instead, and without the ",string" tag!
Regarding the original question, the ",string" tag doesn't work there because the string option "applies only to fields of string, floating point, integer, or boolean types," and []int64 is a slice of integers, not an integer itself.
Here's a solution that doesn't rely on the difference between encoding and decoding json.Number, unfortunately you have to change the type of integer in the slice for it to work; you could then copy the values over to an []int64 slice using a loop if that's required: