@KasumiLover - DOA3 and 2 were definitely backwards compatible for the 360, but only if you had the disc. But I don't think they were for the X1 or Series. The were never true backwards compatible games because you couldn't buy them in the market place.
I don't think they were ever able to put DOA2-4 on the marketplace due to licensing issues? Something to do with TN using Aerosmith songs in the previous games.