How is retirement defined for the purposes of the IRS?
There is no special definition for "retirement."
You may consider yourself as retired as you wish and at any age.
There are some definition of retirement based on specific purposes. Most are based either on age or on years in service or on both.
For instance for social security purposes -
early retirement age is generally started at 62
normal retirement age is between 65 and 67 (based on the year of birth)
For the IRS - for distribution purposes from retirement funds to avoid early distribution penalty - the age is 59 1/2.
Can you retire from work, but still run your own business(es)?
You definitely could - there is no age discrimination from running the business.
If the scenario I described above holds true, why would it make sense for me to have a 401k right now?
I would say - yes - because contributions into qualified retirement plans are limited - I would suggest to make contributions whenever it is possible.
The advantage is that tax liability on earnings inside qualified tax deferred account is also deferred. That is true - you will pay taxes later - but by delaying tax liability - you are kind-of interest free loans from government to use for your investment.
In additional - funds from 401k plan could be converted to Roth IRA. Yes - such conversion is taxable - however earnings inside Roth IRA are potentially NEVER be taxable,
So - there are some opportunities arise from having funds in the 401k plan.