How is Rice's theorem applicable to this decision problem?
As you correctly mention, polynomial running time is not a semantic property. 

However, the property required here is not polynomial running time (of $M$), but functional equivalence to a TM with polynomial running time (on those inputs where $M$ halts). It is of no importance, how long $M$ runs on those inputs. This is a semantic property, since every other TM $M'$, that computes the same function as $M$ will have the property as well: $M'$ halts on exactly the same inputs $x$ as $M$ and on these inputs $M'(x) = M(x) = H(x)$.