Foods don't always categorise tidily, and this seems to be a sort of hybrid. I'd say it's closer to a cheesecake.
Cheesecakes can have a variety of bases, though soft biscuits are rare. They can also have a jelly topping, or, as in my profile picture a thickened fruit topping (cooked blueberries with arrowroot in that case).
In trifle, the biscuits or cake in the bottom layer are normally soakedin the jelly; with some common choices that's the only reason they're soft.
Trifle also usually has whipped cream, no cheese, though whipped mascarpone or cream cheese could easily be used.
Overall I'd probably call it a cheesecake trifle (I wouldn't call it a cake, perhaps a dessert).