Playing Catherine on PSNow with Keyboard & Mouse

tl;dr Not without additional software

I don't know what functionality Parallels offers, but as of the time of writing, PS Now on PC only officially supports the Dualshock 4 controller for input. Some non-Playstation controllers are supported, and some are not (from personal experience, the X-Box 360 and X-Box Elite controllers are, Steam Controllers and Dualsense 5 are not). Anything that is not a DS4 will not have touchpad/gyro functionality.

However, if you're willing to sink some effort (and money) into this endeavor - there is a paid piece of software, reWASD (no affiliation). It adds a virtual DS4 controller and allows you to map non-supported controllers or keyboard/mouse inputs to the virtual controller. I have not personally tried using it to play PS Now with a keyboard and mouse, but I have successfully used it to "trick" my PC into thinking a Steam Controller was a DS4 and used it to play PS Now games (I have had limited success mapping any input to the virtual touch pad but the default, out of the box mappings are perfectly serviceable).