Does receving short term disability insurance payments qualify as disabled to avoid the extra 10 % tax penalty

For income tax purposes, "disabled" means unable to perform gainful work, due to a condition that is permanent, or is expected to last at least 1 year, or that is expected to lead to death.

If you are on STD because you are expected to be able to go back to work in a short time, then you are not disabled for tax purposes including retirement penalties.  However, if you are permanent disabled and your company is paying out STD before switching to LTD, then you are disabled.  The type of policy doesn't matter, what matters is when you might be able to go back to work. 

No. For the IRS, to qualify as disabled, you must be permanently and totally disabled.

You have a permanent and total disability if you can't engage in any substantial gainful activity because of your physical or mental condition.