The problem is with chrome.storage.sync.set({key: testPrefs}

Your data is stored as

{
    key: "{"val":10}"
}

So, your code chrome.storage.sync.get('myKey') return undefined\empty object.

Solution I

Use string "key" as your key

chrome.storage.sync.get("key", function (obj) {
    console.log(obj);
});

or

Solution II

Set data through "myKey" Key.

chrome.storage.sync.set({"myKey": testPrefs})

P.S : Don’t forget chrome.storage.sync is permanent storage API, Use chrome.storage.sync.clear before any further testing to see changes

References

• Storage API

EDIT 1

Use this code to set variable value in Chrome.storage

function storeUserPrefs() {
    var key = "myKey",
        testPrefs = JSON.stringify({
            'val': 10
        });
    var jsonfile = {};
    jsonfile[key] = testPrefs;
    chrome.storage.sync.set(jsonfile, function () {
        console.log('Saved', key, testPrefs);
    });

}

It generates following Output

Object{
    myKey: "{"val":10}"
}