Looking at that screen shot, it looks as if the modem is connected directly to an Ubuntu system and that system has both an IPv4 and an IPv6 address, with routes for both. The modem is likely in "pass-through" mode, given that you've got a "public" IPv4 address and route.
If you can't connect to the rest of the world with that box, then the problem is likely with the ISP and/or modem.
I'm not one to argue, but this modem is "dumb" it has no passthrough. The original DSL (AT&T Motorola NVG599) did have in the router portion a passthrough mode, and the router (Archer C7v2 with OpenWRT/LuCI) was configured originally with that.
I agree -- I've had several modems that somehow "magically" detected if they should be in pass-through mode or in router mode. No clue how they did it, but they seemed to auto-switch to pass-through mode for me. I did find that the boot sequence on the Arris SBnnnn units seemed to have an impact, but I didn't find my old notes on the "right" order. The modems can also be "sticky" as can the DHCP of your upstream provider. I don't know about Time-Warner, but sometimes unplugging everything from Comcast for 10-20 minutes (or worse, at times) and coming back later seemed to help. Good time for a beverage of your choice