Gatwick Express services are operated by Southern.
Open Access TOCs have to accept inter-available ticketing if they want a slice of ORCATS revenue. If they didn't want ORCATS revenue then they'd not be viable. I believe they are called "associate members" rather than "full members" or something like that. I'd guess they get very restrictive voting rights, and they are not entitled to join PRIV discount schemes, but they do have to accept inter-available tickets. Glynn80 is an expert on this I believe, he may be able to clarify.
Open-Access operators are associate members of ATOC but participate fully within the "schemes" managed by ATOC on behalf of the TOCs.
The mandatory schemes are
National Rail Enquiry Service Scheme (NRES)
Ticketing and Settlement Scheme
Certain Railcard Schemes (16-25, Senior and Disabled)
London Schemes
(If applicable)
Rail Staff Travel Scheme
(I believe Open-Access operators are either banned or exempted from mandatory membership to this scheme)
ATOCs remaining schemes are open to operators on a voluntary basis. They are:
Other Railcard Schemes (HM Forces, Family and Network)
International Scheme
Retail Agents Scheme
Operations Scheme
Engineering Scheme
It is the Ticketing and Settlement Scheme membership that includes the obligations to accept inter-available ticketing (including the All Line Rover) and allows TOCs to receive revenue through the ORCATS scheme.
With regard to their voting rights, I believe that Open-Access oeprators get full voting rights [1] within the various schemes they are members of, but do not get voting rights on the ATOC board.
[1] Voting rights in the Ticketing and Settlement Scheme are proportioned to the TOCs income from fares. Voting rights in the individual railcard schemes are based on share of revenues from the use of each railcard.