Hello, If a competitor is setting up obvious doorway pages, that redirect to my domain, can this harm my google rating? Should I tell google?
Personally I would be tempted to notify Google just in case it does harm your rankings. I don't see any other reason for a competitor to do this. Theoretically competitors shouldn't be able to sabotage your rankings, but I'm sure there are some tricks out there that work.
Most often the site hosting doorway pages gets penalized, so your site should be fine still you can contact google and tell your concerns to be on safer side.
Let him make all the doorway pages he wants to that point back to your domain name. Those pages will not harm your rankings as they do not reside on your domain and google will not penalize your site for other domains that point to yours. Those doorway pages will either carry no value to your site and that competitor is wasting their time in the end.