No, you don’t need a solid state drive or an Intel processor - Roon should definitely run on your laptop. However, depending on the size of your music collection, you might not get the snappiest performance. Roughly how many albums/GBs of music do you have?
Depending on the models an A10 has comparable performance to an i3, which is the lowest recommended CPU. Your library size shouldn’t create issues for that level of CPU but you might have issues with DSP or upsampling to all supported resolutions.
Although an SSD is not necessary it is recommended for a reason. Roon accesses the database quite often and an HD slows down performance quite a lot.
You should be able to install Roon on the hardware you have, but the user experience will be less than what is possible with an SSD and a faster CPU.
The CPU is fine for a library of that size, but running Roon without an SSD can be painful. Nothing wrong with giving it a shot, but if you run into performance problems, keep in mind that they may be because of the spinning drive.