Hormann garage door opener automation with Loxone
According to the Guide you posted

The UAP enables you to

control the light of the supramatic
open the garage door
close the garage door
stop the garage door 
check whether the door is totally closed or totally open, light status? 


That tells me that it appears your UAP will not allow for the individual movements that you are looking to achieve.
The only things I get from what is stated is that if you press to open - you press the button again to stop it (not a true move up move down motion).

That being said you might be able to program a button to activate open when pressed and to also activate the same function on release. 

Looking at the other link for the Hormann website using translation - it looks like they indicate it can do a partial open : "for controlling the partial opening and the drive lighting"

I do not see any manual on their site for this unit.

I see one for your supramatic (seems a bit over complicated for a Garage Door) - however reading the instructions for the ventilation position You might find what you need here. http://www.hormann.co.uk/fileadmin/_country/hoermann.uk/dok/SupraMatic_Series_3.pdf

6.1.13 
Menu 43: Changing the 
ventilation position
▶ 
See Figure 
28
The partial opening position (ventilation 
position) depends on the door type and 
is pre-set at the factory.
Sectional door:
Approx. 260 mm slide 
travel before the 
Close
end-of-travel position.
Minimum 
height
Approx. 120 mm slide 
travel before each 
end-of-travel position.
The partial opening position is triggered 
using the 3rd radio channel (menu 13), 
an external receiver, the additional print 
UAP 1 or an impulse at terminals 20 / 23.
To change the partial opening 
position:
1. 
Move the door into the desired 
position with the buttons 
 and 
, 
via the taught-in radio code 
impulse
or an external control element with 
impulse function.
2. 
Select menu 
43
.
3. 
Press the 
PRG
 button until the 
decimal point next to the menu 
number is illuminated.
The changed partial opening position 
is saved.
If the selected height is too low, a 2-digit 
number starting with 
1
 will appear with 
a flashing decimal point (see section 17)