The author cherry-picked the few unfavorable countries.
Most countries on the Pew Chart don't have a rating during both the GWB and Obama presidencies, so the author can't say the rating dropped. In the majority of the other countries, the rating has gone up under Obama.
Where you think it counted - UK, Spain, Italy, Canada, India, Brazil, Australia, Japan . . . - the favorability rating has gone up under Obama. France has not moved.
Okay, I just checked the UK but maybe the rest of them are as you say.
In UK:
The favorability rating 2009 69%, 2014 66%. It’s down.
The unfavorability rating 2009 20%, 2014 27%. It’s up.
Confidence in US President 2009 86%, 2014 74%. It’s down.