While it's possible that the services that Google and YouTube (and others) provide could infringe on copyright, this was actually discussed in the original court of appeals ruling (Svea hovrätt: dom 2010-11-26 i mål nr B 4041-09, see pages 24-25) and the reason given that makes Google et al. different from The Pirate Bay (TPB) goes to the intent of the service provided and legal theories that states that a service provided can be free of liability if the benefit to society is great enough; the primary purpose of Google isn't to facilitate copyright infringement. The court concluded that TPB was used almost exclusively for file sharing so the same grounds for absolving liability wasn't deemed appropriate.
A quick Google translate of the applicable part from the ruling:
"If a search provider is by nature such that it in the first place is a valuable tool for lawful activity and generally socially beneficial,
if the legitimate use dominates, distribution or transmission of illegal materials despite precautions can not be ruled out, the operation of such a service in
objective point of view be regarded as permissible under the aforementioned theories."