What people usually mean by "Turing complete" is "would be Turing complete if it were infinite." That does imply that a programming language can be built on to

What people usually mean by "Turing complete" is "would be Turing complete if it were infinite." That does imply that a programming language can be built on top of it, and that programming language is fully capable of performing any given algorithm. It says nothing about interactivity, which is a function of ability to (directly or indirectly) access I/O hardware.