Does Airport Extreme REPLACE Comcast xfinity box?

If I purchase an Airport Extreme, do I set it up to REPLACE my existing Comcast xfinity box (coax cable in

No, since the AirPort Extreme is not a modem.....it has no co-ax input.....it is a router only.

is it somehow used in addition to the existing box (Arris Touchstone TG862 Telephony Gateway).

Yes, but there is really no reason to add an AirPort Extreme, since your Gateway is actually a modem and router in the same package. If you add the AirPort Extreme, you will have a modem and two routers.....probably something you don't need.......unless you need more wireless networks.

I'm having troubles with my ProAnalyst 6.4.7 charting program that receives real-time market data but is displaying it incorrectly. The charting program developer says I'm the only one in the USA with this problem, so if I can replace the whole Comcast Arris box, it might just solve the matter.

Adding an AirPort Extreme to your Gateway will not solve this issue. Perhaps a different model or brand of gateway might solve the issue. You would need to check with Comcast about this possibility.