For this special case of the split vector layer algorithm, before QGIS 3.10:
- You need to update the code as mentioned in the other answer.
Since QGIS 3.10, the parameter is back and working:
For usual Processing algorithm, any QGIS version:
You could let the default output memory layer when you launch the algorithm. And only after your analysis, in your legend, right click on your layer,
export and then
Save features as. You can choose the format you want, such as shapefile.
Or, you can simply choose the format your want before to run your processing algorithm