Do you feel that this definition should be made more specific or is this a common use of the term?

Goo·gle
, Goo·gled, Goo·gling.

verb (used with object)
(often lowercase) to search the Internet for information about (a person, topic, etc.): We googled the new applicant to check her background.

verb (used without object)
(often lowercase) to use a search engine such as Google to find information, a Web site address, etc., on the Internet.
(Dictionary.com)

Should these entries specify that the term googling refers explicitly to using the Google search engine (such as in the Miriam webster dictionary) or is it appropriate to use the term “google” as a verb when describing using any search engine (such as shown on dictionary.com)?

And why is the term googling not included in the google chrome spell check library?