I think the definition has always been a bit gray, even more so in recent years but I don't think it's about the hardware present in the device. For example, Sony made a push to classify the PS2 as a computer by providing a BASIC interpreter and later a distribution of Linux to evade some tax laws in Europe.

I think if I were to answer this question now it would be based on the expectation of the end consumer to be expected to, or have the ability to program the device for general purpose tasks.

Things like game consoles, phones, smart appliances, etc. all start to blur that line but I think it comes down to the consumer's expectations.