My interpretation is that the Plant Room is common property however that does not mean that all Lot owners have access to it. Your building plan would probably have this area designated as a Plant Room. To change the use of this area to a gym would probably breach the development consent, building regulations and the planning regulations. Have you sought advice from your local Council?
It is not unreasonable to place restrictions on access to some common property if that area of the common property contains services. Clearly your safety audit has deemed the use of this space for a gym to be a hazard.
The Motion that the gym equipment owner has proposed can be ruled Out of Order if it breaches regulations.
In addition to breaches of the NSW planning regulations in my opinion the gym equipment owner has breached SSMA 2015 [s108(2)].
108 Changes to common property
(1) Procedure for authorising changes to common property An owners corporation or an owner of a lot in a strata scheme may add to the common property, alter the common property or erect a new structure on common property for the purpose of improving or enhancing the common property.
(2) Any such action may be taken by the owners corporation or owner only if a special resolution has first been passed by the owners corporation that specifically authorises the taking of the particular action proposed.