Yes the estimate assumes you will work till 62,67,or 70
I recently ran some numbers and in my case at least, retiring at 62 or 70 makes little difference (less than 2%)
The estimates are also low-ball in that it assumes no inflation between now and your retirement. For example for 2020 contribution is capped to $137,700. The SS sheet in 2020 assumes that it will stay that way between now and retirement, but the 2021 number is actually $142,800.
I like https://www.bogleheads.org/forum/viewtopic.php?t=262772
because it takes an educated guess at what future limits will be.