Is a sub panel necessary to wire this 10.5kw 43.75amp sauna heater?
Normally you'd need the sub panel if for no other reason than to have a means to disconnect the sauna for maintenance. Since the sauna is in the same room you can go directly to it from the main panel as long as you have clear line of sight from the panel to the sauna. 
Your instructions show a sub panel and you shouldn't deviate from them but they also give wire sizes for going from main breaker to power unit (4#8,N &amp; G) so I guess it's OK. 

I think going to the sub panel would be cheaper.