How to restore replication after server crash
In the end I simply did what the server wanted, i.e. created all the "publication" tables (*dbo.MSpeer_** and *dbo.sys**) in the problematic database (the one that was the publisher), through Script Table As -> CREATE To dialog. Thanks to this server allowed me to disable publishing and distribution. Then I only needed to reconfigure replication. 

Hope, next time it crashes (actually I hope it won't), we'll be wise enough to backup tables involved in replication thoroughly.



Additional information by Zane, originally left in a comment:

The tables dbo.MSpeer_* and dbo.sys* can also be created by configuring the distributor/publisher on a different server with SQL Server installed. This will create these tables in the database that you've set for publishing. See -> Tables - >System Tables in SSMS.

Then, generate the schemas for all these tables and then create these tables in the problematic database which will allow you to disable distribution and publishing and reconfigure the distributor.