It seems you're getting confused.
I just forgott the most important link. My mistake. Maybe that makes it
a bit more clear.
http://wiki.openstreetmap.org/wiki/Key:internet_access
And there you can see that the advice so far is to tag Internet Cafes as
amenity=cafe + internet_access=terminal
In my opinion that is not a "Internet Cafe", but "A cafe that offers
internet access".
If, as it appears in your photos,
these establishments don't serve beverages etc then they're not Internet
cafés, just places you can get access to the internet.
But that is the common usage of the word internet cafe. In the first
place it's a place that has several computers with internet access. In
addition to that it might offer drink&food.
http://wiki.openstreetmap.org/wiki/Tag:amenity%3Dinternet_cafe
Which was created by me this morning, when I found serveral of those
tags on tagginfo.
The statement "Internet cafés are primarily cafés" would be more
accurate if 'are primary' was replaced with 'include'.
I'm assuming you looked at amenity=internet_cafe? The quote came from
the other wiki page where the advice was to tag as amenity=cafe +
internet_access=terminal, which was my problem. But yeah I caused some
confusion by missing that one link I guess...
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