I see you ave deverter on the roof, that might have worked better if it was on an angle to direct the water to one side or both.
A gutter would help with moving roof water away and stopping some of the splash up on the door.
But it will do nothing to protect against wind drivin rain,
Some problem you have, the deck should have been a full 6" below the door unless it is covered with a roof.
It is important to get water to move away from the door as fast as possible and the bricks as nice looking they may be allow water to sit against the threshold.
Usually we want the door installed over a pan that will pick up water that enters anywhere around the door and let it run out under. So we don't usually see caulk under the threshold.
This looks like the splash up was getting under the threshold and some one was trying to fix that with the brick, fix one problem, and cause another.
So a gutter would help, check the caulking around the door might stop some water, the real fix here would be some sort of roof over the area.
Have to agree.
At least 95% of the time when pulling out patio doors I find they where installed wrong.
Here's what a sill pan looks like. http://jamsill.com/
I've made a ton of money off of this one building 101 mistake fixing all the damage caused by someone not taking the time to do it right.
The only right way to fix it is to remove the whole door.
You always should have a gutter to prevent damage to your foundation... could be a huge problem down the road. You will have to maintain them regularly, but there are ladder-less tools you can use like www.ezsmarttools.com