Hi @Benjamski I'm no expert of the log output so can't comment, but I had problems, I reinstalled a clean copy from here, which I think is the 'official' location and then followed the instructions to create the two directories, which is the bit you're stuck on?
If that is the bit you're stuck on, then in more explicit language this is what I did:
open Finder
from my Home folder (in my case Macintosh HD > Users > Alan), I clicked to open the folder `Library`, it may be hidden, if so then
click to select the folder Macintosh HD > Users > Ben (assuming that's your home folder)
in the Finder menu on the menu bar click Go > Go to Folder and in the drop-down type 'Library' (without the quotes) and enter
you should now find your Finder window is showing the contents of your Library folder, so now you should be able to click to select Application Support > Alfred a > Workflow Data
in the 'Workflow Data' folder create a new folder called precisely
carlosnz.eggtimer2
so that's no spaces or uppercase
now use Finder to choose the same Library folder (just below your home folder) and this time click to go into the
caches
folder, and in this folder create a new folder called precisely
com.runningwithcrayons.Alfred-2
with these two empty folders created, quit/restart Alfred and try the Egg timer again, for me it then worked AOK
Good luck and hope this was helpful and not stating the obvious!