I'm also a Spotify developer. I think there has been some misunderstanding here; we've changed the autoplay behavior such that the client will not autoplay links if the user is playing something else. On the one hand, this is indeed a usability issue since users who were accustomed to the old behavior need to double-click the highlighted track to play it. However, we considered the old behavior an even worse usability issue, since clicking any Spotify link on the web was likely to interrupt your music (or "context hijacking" as we nicknamed the phenomenon).
Although some people liked autoplay, many others did not, and as a result these users were inadvertently trained to avoid clicking any open.spotify.com links at all. For this reason, we changed the client to not autoplay links if it is already playing something. Also, this is more consistent with other media players.
That said, if the client is not playing anything and the link does not play, then it's a bug. Also, directly clicking a play button on a site such as open.spotify.com or last.fm should also play in the client (I just tested this and it works for me). However pages that are automatically opened in the client should not be played or hijack the play context.
We have heard some reports about WebHelper not correctly playing links when the client is paused (this seems to mostly happen on Windows). Also I would be interested to know if Spotify was already running or had to be launched by WebHelper. Can you provide some more details on the situation?