In the national income accounts, personal saving is defined as income less taxes less consumption. So if there's new money going into a 401(k) - new in the sense of coming out unconsumed current income rather than just being shifted from a bank account - then it does count as personal savings. Employer contributions to pension plans also count as personal savings (in the national income accounts, the contributions are included in the category "other labor income").
Capital gains do not count as savings because the concept underlying the national accounts is that income is the reward of production; all income must be matched with production. So, conceptually, savings are unconsumed income, and investment is unconsumed production - or as Keynes said, savings and investment "are merely alternative names for the difference between income and consumption." Cap gains don't originate in production, and any expansion in wealth from cap gains is just the result of existing assets being revalued; there's no analogous increase in the stock of physical capital, and no deferral of consumption.
So the point of pointing to the low savings rate is that there isn't a lot of tithing going on, or, even if there is, the profligate are borrowing more than enough to outweigh the prudent.
I'm typing this as a Stein Roe ad for a new mutual fund for kids is running on CNBC.
Doug