No one claimed that. The point was that Valve controls the API and can cut access to said API to the gambling sites. This is not like sports betting, where the gambling sites don't need any integration with the actual sport : if Valve wants, they can seriously affect the abity of the sites to function.
Yes, they provide the API that those sites need to function. That doesn't mean the API is exclusively for those sites. Just that Valve is the one enabling those sites, they're not completely independent.
Nonsense argument. They provide an api that players use, that can also be used by boys to perform trades. Maybe the problem you have with this is that they can do trades.
I really don't get what you're confused about. Yes, the existence of the API is good and useful. What Valve should do, if they really cared about stopping CS or TF2 gambling, is to limit access to this API for the gambling sites. The API should ONLY be accessible to individual players. That means IP restrictions, client agent sniffing, bot behavior analysis, etc - not trivial, and not foolproof, but also not exactly rocket science.
