Update an array element with inc mongo update
I accomplished it with your criteria which was to use the tags field in your query. I of course had to filter on the document further to only update that specific document. 
I presumed other documents may have a tag of "famous". I created two documents with tags:famous to prove this worked when updating 1 document. Here's my solution with comments.

//basics 
db = test
collection = test

//data looked like this with two documents for testing
/* 0 */
{
    "_id" : ObjectId("5498778567bbbc2fff723515"),
    "articleId" : [ 
        {
            "articleId" : "9514666",
            "articleCount" : 1
        }
    ],
    "count" : 1,
    "timeStamp" : "1416634200000",
    "interval" : 1,
    "tags" : "famous"
}

/* 1 */
{
"_id" : ObjectId("5498781567bbbc2fff723516"),
"articleId" : [ 
    {
        "articleId" : "951466622",
        "articleCount" : 22
    }
],
"count" : 1,
"timeStamp" : "1416634200000",
"interval" : 1,
"tags" : "famous"
}


//confirmed I can query the one document like this
db.test.find({'tags': 'famous','articleId.articleId':'9514666'})

//was able to execute an update as described
db.test.update({'tags': 'famous','articleId.articleId':'9514666'}, {"articleId" : [
        {
                "articleId" : "9514666",
                "articleCount" : 4
        },
        {
                "articleId" : "9514667",
                "articleCount" : 3
        }
],

"count" : 7,
"timeStamp" : "1416634200000",
"interval" : 1,
"tags" : "famous"
}) 


//Resulting update to document is
/* 0 */
{
 "_id" : ObjectId("5498778567bbbc2fff723515"),
 "articleId" : [ 
    {
        "articleId" : "9514666",
        "articleCount" : 4
    }, 
    {
        "articleId" : "9514667",
        "articleCount" : 3
    }
],
"count" : 7,
"timeStamp" : "1416634200000",
"interval" : 1,
"tags" : "famous"
}

//showing both documents, only first one updated obviously
/* 0 */
{
"_id" : ObjectId("5498778567bbbc2fff723515"),
"articleId" : [ 
    {
        "articleId" : "9514666",
        "articleCount" : 4
    }, 
    {
        "articleId" : "9514667",
        "articleCount" : 3
    }
],
"count" : 7,
"timeStamp" : "1416634200000",
"interval" : 1,
"tags" : "famous"
}

/* 1 */
{
"_id" : ObjectId("5498781567bbbc2fff723516"),
"articleId" : [ 
    {
        "articleId" : "951466622",
        "articleCount" : 22
    }
],
"count" : 1,
"timeStamp" : "1416634200000",
"interval" : 1,
"tags" : "famous"
}