It's pretty simple. The 10% is any savings for retirement.
Preferably, it's in a retirement account, but that's not mandatory.
It's great that you save for a vacation, computer, house deposit,etc, but that's not what these articles are referencing.
Edit (in response to the running comments on @BrenBarn's answer)
The mortgage issue is worth further discussion. I'm saving toward a home purchase, it may be $50K saved. But that's not money for retirement, the house savings never is. I get the $200K mortgage, my balance sheet is net neutral (less fees, closing costs, of course) but my retirement savings again is unchanged. I put $10K toward principal, the balance sheet again is $10K better, but retirement account, unchanged. Last, I pay off the mortgage. Retirement account unchanged. But, my retirement budget requirement is $1000/mo less (The mortgage payment), and my 'number' drops by $300K or so. (This is based on the 4% rule. To withdraw $1000/mo requires $300K in retirement assets.)
It may seem pedantic, but there's an important distinction to be made here. It's easy to distinguish retirement savings from all other wise financial transactions. Paying debt off is wise but not retirement savings. Any actions that reduce your ongoing expenses? Clearly, wise. And it reduces the number needed to cover your retirement budget, but it's distinct from 'retirement savings.'
For those that enjoy the intellectual exercise of insisting there's always a grey area, I'll give it to you. The family with 3 kids, in the $1.2M 5 bedroom house. The parents know they will move into their paid off summer house upon retiring, and sell this family house. In his wisdom, hubby has planned for the mortgage to be paid in full well ahead of retirement, and for purposes of planning, only view the house as worth $900K. The house does have a relationship to the retirement savings. But the action of planning for Alice's retirement (the maid they will no longer need once they move) is not savings, but rather, an adjustment down in their retirement budget.
I think you'll find most conflicts regarding this issue resolved by understanding this distinction.