Can I use casserole steak instead of braising beef for this Chinese Beef Casserole recipe?

For the recipe you are using, any flavorful cut of meat that is up for long cooking should work okay. Had to look up casserole steak as that is not something I've ever seen in the US, at least not by that name.

From a Jamie Oliver forum , please see the following:

Braising steak is often used in a casserole. Mostly nowadays "Chuck" steak is sold for braising steak and is often used in "Casseroles". This is a cut of beef from the "forequarter" of beef and is the shoulder piece of the beast. It contains a fair bit of fat which is normally rendered down and incorporated into the dish. Sometimes the "Blade or LMC (leg of mutton cut)" is also sold as braising joint of beef......which is on the other side of the blade bone to the Chuck steak but is very lean and somewhat void of flavour.

Stewing steak is nowadays mostly "shin of beef"....which is what is says...shin. This can be from the forequarter or the hindquarter of the beast. It differs quite a lot from braising steak as it contains a lot of sinnue and membrane which separates the individual muscles within the cut. All these sinues render down in cooking to give a gelatinous addition which a good stew requires. You are more likely to see the hindquarter shin for sale as stewing beef as the fore-shin is usually taken for sausagemeat or burgers etc....along with the neck (clod) and skirt which we don't really see anymore.

The terminology may or may not be exact, depending on where you are located, but again, any cut that will stand up to long cooking should work.