My 401(k) offers a number of options - stock, T-bills, bonds. The plan, however, only pays out in CASH!
The White House and their posted plan do not tell us about 401(k) plans. I suspect their intention is to not adjust 401(k) "at this time" (if ever!)
It can come out in cash or in company stock certificates depending on the plan. The bigger issue is self-directed IRAs invested in dividend paying stocks, and the tax on THOSE dividends.
When eligible I highly recommend removing your 401k money and reestablishing it in an IRA using direct transfer. After doing some research on 401ks, I find that most of the benefits and not mandated by law but only serve at the pleasure of your employer........like getting your money prior to age 65 for example. The next time your company is bought out or taken over, the benefits may not be the same anymore. I would never leave the money with the company after I left.
I do not believe there is any way to make a withdrawal from a 401(k) in anything other than cash, nor do I expect that requirement to change.
However, depending on how long you've been working, you may have other sums in your account that are treated as post-tax dollars, and those will receive a different tax treatment (they won't be taxed) when you withdraw them. It's not a big deal to lump any future dividend payments within those accounts into that same "tax-free" status.
I haven't seen the text of the President's speech, but apparently he didn't mention this aspect at all. In any event, these are the kinds of details that would necessarily be addressed in the legislation to be introduced.