Not sure LudovicC.
The statement on the manual on that page initially is: "Hardware differences between v1, v2 and v3 modules affect flow match and capabilities.". The word "Hardware" make me think that at HPE/Aruba they are referring to v1, v2 and v3 zl Modules Hardware differences (ASICs generations changed between v1, v2 and v3 on zl Modules) that affect flow match and capabilities (indeed they also refer to "OpenFlow fields/actions that can be matched/executed in Hardware").
Grouping v2 and v3 (2nd and 3rd Generations) separately from v1 (1st Generation) make me also think that at HPE/Aruba they refer to something that is Hardware related and not Software related since - exactly - v2 zl Modules and v3 zl Modules support features that simply v1 zl Modules don't...so this way of grouping seems something rational.
Aruba 2920 is excluded from that since it doesn't support any zl Modules...so all those speculations could be relevant only to use OpenFlow 1.3 specifically on HPE/Aruba 5400 zl, 8200 zl and 5400R zl2 switches equipped with/without v1 zl, v2 zl and/or v3 zl Modules.
It seems HPE/Aruba published an updated "HPE Switch Software OpenFlow v1.3 Administrator Guide - K/KA/KB/WB/WC 16.02" (June 2016) for Platform letters K, KA, KB, WB and WC (Note: WC is used by Aruba 2930F Switches Series for which I'm unable to find the Software Download or Release Notes), look here.
Also note that - actually - the 16.02 isn't officially released (latest available Branch - I think it is the GA branch - is actually the 16.01 derived from the 15.18).
Edit: corrected Aruba 2930R into Aruba 2930F.