I'm sure the line check does not count because a line check under FAR 121.440 doesn't. And the Swiss type doesn't either. 61.56 says a check given by an Examiner. 61.1 defines the term Examiner:
(5)*Examiner*means any person who is authorized by the Administrator to conduct a pilot proficiency test or a practical test for an airman certificate or rating issued under this part, or a person who is authorized to conduct a knowledge test under this art.
I'm willing to bet the examiner who gave you the Swiss type did not hold a letter from the FAA.
61.56 gives guidance s to what a flight review is made up of, at least one hour gound study and one hour in flight. Since your FAA certificate was issued in 2010, it's not current until you complete a FR or do one of the other things listed in 61.56 with a FAA instructor or examiner.