If that is the case then it's ridiculous. The card in use matches all the criteria of any that Cycliq recommend.
To be honest though it all seems a right faff as well. Fitting, removing, fitting to second bike, removing to charge, wondering the whole ride if it's working or not
So from dipping my toe in the water I'm very happy to scrap the whole idea and go back to the dark ages, it's a far simpler place there
Some additional thoughts from my ride into work this morning. as my post at #71 was made just before I went to bed.
Cycliq supply a 2Gb card with the camera. I would try formatting the supplied card and doing a factory reset. If the camera records with the 2Gb card but not with your 32Gb or 64Gb cards, it would look like your cards are incompatible. You might also want to check the version of the software on your camera, with the last release according to Cycliq.
If it looks like the cards are incompatible it's your choice about what to do; probably driven by why you bought the unit in the first place. Personally for a few £s I'd keep it. - I have a couple of cards which are "live". A couple of weeks ago I managed to misplace one of the cards between my garage and lounge. The Cycliq compatible 64Gb replacement, was £6 more than the card you linked to.
If you are swapping between bikes, whilst the unit isn't as user friendly as (say) a Garmin, if the unit remains attached to one half of the bracket, isn't it just undoing a couple of allen head bolts?
Don't get me wrong, I am not a Cycliq fanboy. For the first few days after the purchase of my original unit, because of the number of factory resets I did, a sewing needle became my new best friend, before I gave up with it and acquired a replacement. Sure it could be improved, but it now does what it was bought for in the first place.