First of all you are mixing different things up. RB260GS is not operated by RouterOS but by SwitchOS (not dualload capable as far as I know). SwitchOS can not be managed with winbox but only with the browser.
The switch does not need internet access at all because he has nothing that relies on internet access. It is a switch, nothing more. The only thing you will need some kind of internet access is for a SwOS upgrade. But internet access is not used as usual, I guess the PC connecting to the switch is somehow used as somthing like a proxy. This is kind of strange for me and it doesn´t work well all the time, but you always can use the manual upload field.
If you don´t have internet access on your Windows PC you probably missconfigured something. If you do not know where to start, then reset the Switch to factory defaults (and SwOS 2.0). Afterwards you have to upgrade to v2.7 and DHCP again. But at this stage (if you did not configure anything else) it is still a dump switch. No port isolation, no vlans, nothing. Each port can talk to each port like with an unmanaged switch. Has nothing to do with a proxy server.