Since the chrome webstore doens't seem to have button to click and submit the search, you could, instead, send the carriage return character and get it to trigger the search result. Try something like this:
var client = require('webdriverjs').remote();
client.init()
.url('https://chrome.google.com/webstore')
.setValue('#searchbox-input','sampleapp \u000D')
.end();
The "\u000D" is just a carriage return unicode code.