Considering every other Sail/Rail combination including ones operated by Stena allow bikes, it seems odd that this one specifically doesn't.
Think this may be the reason. From the Stena website:
Route Hook of Holland - Harwich
Abellio Greater Anglia does not carry bikes on trains which arrive in London between 07:45 and 9:45* and depart from London between 16:30 and 18:30*.
For passengers who have a ferry and train ticket and travel by bike the first possible departure by train from Harwich International is at 8:33 and from London Liverpool Street station at 19:00 (change trains in Manningtree)
Unsure why they couldn't just put a specific T&C around those train times. Guess it's too much hard work and people may kick up a fuss if they don't adequately read the terms.
Hm, thinking about the others
Sail-Rail GB to ROI via Holyhead: Any UK to any ROI station and v.v. (It's a National Rail and Irish Rail thing from the days of international rail co-operation)
Sail-Rail via Redhouse Point: Any scottish station to Belfast and v.v. (Its a Scotrail and Stena thing, possibly a legacy of Sealink but Translink is "different")
Dutch Flyer: Any Dutch station to London and v.v. (But then this is also a Sealink legacy of BR and NS co-operation)
So to use that ticket you have to use a London station