At last a sensible post, Im not entirely sure, I personally Didnt know there was one, but I doubt there is, if you pop in to Tourist information they will have leaflets or books with information on the youth clubs in Dawlish so pop in and I'm sure they will not only answer your question but tell you were there is one.
Recommend you ask Town Council, but as far as I know there is still a long way to go re raising funds. If you feel like it have a look at the proposed building in the planning part of Teignbridge District Councils website. One of the reasons why this is going to be a long process is the proposal to put the skate park under the building. Keeping it under cover is a good idea but it puts the cost up by huge amounts and means that it only accessible when staffed. Bit daft when the kids just want ramps etc and are desparate for somewhere to go.