Characterisation of Turing completeness? I know the definition of a Turing machine but I am trying to find a practical way to characterize a Turing-complete language.

For example, an imperative language is Turing complete if it has conditional branching (e.g., "if" and "goto" statements, or a "branch if zero" instruction) and the ability to change an arbitrary amount of memory (e.g., the ability to maintain an arbitrary number of variables). That gives an easy way to say if a language is Turing complete, as soon as we've found out that it is imperative.

Hence my question is there any similar, characterization of Turing completeness which would work for any language?
It seems very unlikely that there is any useful characterization other than the definition. Any such characterization would have to deal with all kinds of programming languages (imperative, functional, declarative and everything else) along with, assuming the claims from the Wikipedia article you link are correct, Minesweeper, Conway's game of Life and Magic the Gathering.

If you did have a characterization, it would probably be no easier to apply that characterization than to just apply the definition.