Logic Pro is a professional application that is available very cheap, so that professionals and amateurs alike can use the same tools. This is because the cost is subsidised by the cost of the mac computers.
A reciever that has optical, coax and HDMI would be a consumer grade home theatre system. Mixing to 5.1 is a highly specialised task, and you are very unlikely to get good results through a home theatre system, even if you could plug it straight in.
Professionals who do 5.1 mixing with Logic (I am one of them) would have a serious multichannel external audio interface, and would plug the disctrete outputs from there into a monitoring system setup in a properly designed room. Anything less would result in a mix that would sound different everywhere it is heard, and probably only good in your room.
The mix as done by logic provides a file or files that are 6 discrete channels. You would then use a program like "Compressor", (previously available with Logic Studio and not to be confused with an audio compressor) to convert the files to one of a number of possible formats.
The format that your receiver would be looking for would be a Dolby digital format, a licensed format designed especially for home theatre. If every mac was designed to deliver that natively so the very few who might use it are able to access it directly, every mac user would have to pay more. This wouldn't make sense.