For the OP........ many things are based on definition. So as long as whoever talks about 'amplification' is clear about what they mean (ie. mathematically, or whatever), then that's fine. If the transistor circuit has a defined input.... voltage ..... or maybe current, and if the output is defined (ie. a voltage or a current)..... and if circuit theory allows us to describe the behaviour between output and input in some kind of mathematical way, or some kind of graphical way, then that's a nice start. Then, on top of that, if changes in output happens to be relatively linear with changes in input, and if the output happens to be significantly larger than the input, then that could be what you call linear amplification. Otherwise, if relatively non-linear relation is seen, then it could still be considered as amplification if the output is still larger than the output.....except it could be called non-linear amplification, or some kind of amplification with a limiting effect.