The info-graphic you linked to is misleading.
The apparent premise is that you should not redirect to a site if the platform is different, structure changes, design changes, or the content changes. This is about as far from the truth as it can be. Of course there are considerations, but none of these items are game changers.
For example, given a structure change, a blanket redirect from the old site to the new site with redirects on the new site to the appropriate URL or page is perfectly reasonable and acceptable. Yes there are two redirects, but this is completely normal these days. For pages that no longer exists, it is perfectly acceptable that they 404 or 410 on the new domain.
The platform has no baring on the matter. Neither does the design. As well, it is perfectly normal that content will change as a company re-brands their site or anywhere thereafter.
Language and content can be an issue only in respect that for a period the site must be re-indexed and the sites semantic metrics reassigned. This is an expense of course, but not a game changer in the least.
If I were building this info-graphic, I would not have made those squares red. It gives the wrong impression. For me, they would have been yellow or some other cautionary color, but not red. As well, I would have broken these squares into something more explanatory so that it is clearer where any caution exists.
There is no linkage or correlation between a redirect and how the site is presented. Period. Removing the redirect for the sake of argument means only that the site has changed just like any other site does from time to time. This is perfectly normal and reasonable.
Doing a blanket redirect, whole site and not just pages, will preserve much of the value of the original site and project it onto the new site. This is a common tactic.
I often offer this bit of advice however.
For any new site, it is inevitable that the old site will want to be deleted. It is far better to assess the link profile of the old site and modify the links you can, and replace the links you cannot modify so that the link profile of the new site exceeds the link profile of the old site. The reason for this is to allow freedom for the time when the old domain is deleted. If the old domain is never deleted, you will not suffer from the additional work. You will gain from it.
It is very common to do a blanket redirect from an old site to a new site and everything has changed. Think of the effect without the redirect. The same effect applies as if you simply changed the site. The search engines will have to assess the changes and update the index accordingly. As well, all the metrics within the index will be recalculated. This is completely normal. The degree of disruption is dependent upon the degree of change.
Assuming you are redirecting the old site to the new, you have the added benefit of some of the site metrics remaining as they are. This includes important metrics such as trust metrics. This would of course changes when the redirect is removed. For this reason, you have two choices. One, keep the redirect for a period or forever. Or two, just pull the band-aid quickly and get it over with. It really has everything to do with the metrics of the old site. The SEO effectiveness of the old site would need to be assessed. If the old site enjoys a reasonably decent link profile and trust metrics and all that remains is on-site SEO (good or bad), then you are in good shape. Just changing the site will fix this (redirecting to the new site). However, if the old site is poor in it's link profile and there is not much value in the trust metrics, then it might be better to simply drop the old domain altogether. There are points in between where it is ideal to at least think about it for a while. I am a firm believer that only redirects from reasonably strong sites should exist. Sometimes the cost of dropping the old site is the same as just plain starting over.
You have to take SEOs with a lot of salt sometimes. Often, they are not technical people and can get a bit wild with their assumptions. MOZ is no exception and in fact, is a site that I find contradicting from time to time. While MOZ enjoys a good reputation, it is not one I advise putting too much stock into. It is not on my short list of sites that I trust.