In general USB3 cards do not require a Mac specific driver. I have a Sonnet USB3 card which does have a Mac driver but the Mac driver is only responsible for activating a higher power mode for the ports to allow charging say iPads, it is not needed for normal use. I deliberately chose the much more expensive Sonnet card because it is one of the only trustworthy makers that explicitly states they are El Capitan compatible. Based on end-user reports most if not all generic USB3 cards do work eve in El Capitan but I wanted to play safe.
Therefore no driver might be ok, have you actually tried to connect a USB device via the card, e.g. a Mouse? A mouse needs minimal power is a simple standardised device and if like nearly all current mice it is an optical mouse would give an immediate visual indication that something is happening as the LED will light up.
Now with regards to USB3.1 cards the picture changes, these cards did initially work under Yosemite although it was not clear whether USB3.1 speeds worked or only USB3.0 speeds. Unfortunately with El Capitan Apple have deliberately disabled these cards from working. No USB3.1 card has any Mac drivers - at least yet.
The disk you are listing the folders from appears to list drivers for all their products, I can also tell that many of these drivers are likely to be generic drivers written not by the supposed maker of the card e.g. Delock but the maker of the main component of the card e.g. ASIX. ASIX for example make the main chipset used in many USB to Ethernet adapters including the adapter made and sold by Kanex Live.
It is extremely unlikely any of those drivers on the disk are for this USB card.
Many USB cards have connectors for power, this is because power needs to be provided to the USB devices plugged in to the card, in particular a USB3.1 card needs more power than a USB3 card and might need more than the PCIe slot itself can provide, so these connectors allow providing additional power to the USB card. Even though many USB3 cards have such a connector I do not believe it is necessary to use it. If one looks carefully at the right-hand edge of the following Sonnet USB card you can see where a power connector would have originally been intended to be, however it is clearly not there. This by the way is what my card looks like.
