Microsoft is mostly to blame for this. It comes down to very poor marketing and naming of products.
Originally and for many years, Office 365 was a marketing term used to represent the services (onedrive, office online, outlook webmail, etc.) and desktop software (Office 20xx) packaged together. Just recently they changed this so that now Office 365 personal and business subscriptions install a more frequently updated and feature rich version of the current stand alone version of office rebranded as Word/Excel/PPT, etc 365 instead of the year versioning.
The point of this was to give MS a steady cash stream instead of a burst of cash every few years from a new office release. The benefit for users is you still get the full benefit of the desktop software which is automatically kept up-to-date (no more upgrading from 20xx to 20xx versions manually) and access to cloud storage and services (onedrive, office web apps, email, etc.) without a big upfront cost.
For all of those suggesting use x, y or z…the sad truth is there is nothing thats 100% compatible (or even close) with feature parity to MS Office. Sure if your writing a 1 page letter or doing a simple 1 sheet table then use whatever. In the business/real world you need to work with others, both inside and outside of the company. The defacto tool for things like large/complex documents, spreadsheets and presentations is MS Office. I can name 3-5 tasks I did in office this week alone at work that I could only have done well and that others could use in MS Office.
As for the OP, are you sure you are trying to install the proper version of Office 365? The link you provided is for the ProPlus 2016 version. If you have an Office 365 personal account you likely downloaded the Office 365 personal version which is based on 2019 but branded as Office 365. They have another link for that https://appdb.winehq.org/objectManager.php?sClass=version&iId=36804 which seems to apply to the 32bit version only. Also the link you posted is only for the 32 bit version of 2016 it seems, so make sure you didnt grab the 64 bit installer.
Personally, I just use KVM and a Windows 10 VM with Office 365 installed in the now rare case I need it. I dont even keep the VM on my machine, but on an external USB3 SSD and only hook it up when needed. It runs 100% proper this way, I am not concerned with updates breaking it and its pretty easy to setup and manage. I may eventually look into doing it with wine, when/if it runs without issue. Problem is when I need it, its for things like pivot tables, PowerQuery, Data models and VBA among other things that I just dont trust to work or be all that stable in Wine.