I prefer referring to static methods via the class name and not this because this conveys an instance member and not a static method. (same thing other places).

Done

I think map makes more sense here

return keys.map(key => ({[key]: this.get(`${baseJsonPath}.${key}`)});

Your code and his are not equivalent :)

return keys.reduce((acc, k) => {
  acc[key] = this.get(`${baseJsonPath}.${key}`);
  return acc;
}, {});

might be more correct but more verbose.

I actually spent a fair bit of time figure out what the best way to do this function was, I was torn between the reduce and forEach. The reduce also needs a typing for the accumulator:

    return keys.reduce((acc, key) => {
      acc[key] = this.get(`${baseJsonPath}.${key}`);
      return acc;
    }, {} as { [k: string]: any });

All the same to me though, I left the forEach for now but will change if there's a preference.