plugin is not defined directly in the array, it is defined inside the object in the array.
Use the Array#find to check if any element in the array contain the given property.
array.find(o => o.hasOwnProperty('plugin'))
Use hasOwnProperty to check if object is having property.
let array = [{"plugin":[""]}, {"test": "123"}];
let res = array.find(o => o.hasOwnProperty('plugin'));
console.log(res);
As an option, you can also use Array#filter.
array.filter(o => o.hasOwnProperty('plugin')).length > 0;
let array = [{"plugin":[""]}, {"test": "123"}];
let containsPlugin = array.filter(o => o.hasOwnProperty('plugin')).length > 0;
console.log(containsPlugin);