Yes, it is dangerous, but there's not really anything you as an end user can do about it if you want to use this software (the fact that tech support considers this 'normal' means it's a known issue on their end which hasn't been addressed by the development team, so no amount of you complaining is likely to change anything).
If the game itself has to run with admin privileges and there's no way around it, then that's a red flag and you should be avoiding it (no matter how popular it is), because that usually means it's using a rootkit or similar technology to deal with cheaters (which is in and of itself a questionable but moderately standard practice) or that there's an design problem with the software itself that the company does not want to fix (an MMO I used to play had the second issue, the client created a folder directly under C:\ at runtime for storing temporary files, and as a result you either had to have things set up just right or run the game as an admin to make it work).
If it's just the installer having to run with admin privileges, I wouldn't be too worried. Most installers need this to some extent, although it is reasonably unusual for one to have to be manually run it as administrator (though not unheard of, the primary software product of the company I work for is like this, largely because it does a few things that regular UAC elevation won't allow).
1If tech support says it should run as admin then it probably needs admin rights like so many other software. – None – 2018-03-02T16:22:27.740
Give it a try if the tech support is someone whom you trust. – iTechieGamer – 2018-03-02T16:24:56.020
2“I am using a 3rd party application for personal work.” “The application is a popular game and I prefer not to give its name here.” Hmmm… I know you don’t want to ID it, but I will say this: I see games as being one of the worst vectors for malware since developers of games are a dime a dozen and who knows what this app will do if it somehow needs admin rights just to run. What kind of development QA process would allow that to happen? – JakeGould – 2018-03-02T16:51:39.997
This game worked fine on a different computer, but I don't know if it is relevant to put that in the question. – Anne Aunyme – 2018-03-02T17:03:07.393
(1) You’re using a game for work? What is your job? (2) An application can do some damage if you run it under your privileges, so you shouldn’t be running it at all if you don’t trust the author. You have to decide how much you trust the author, and, since you’re not telling us any details, we can’t help you decide that. (3) I agree with JakeGould: this seems very suspicious for a game. Is tech support willing to tell you what the application does that requires privileges? (3a) If this tech support for the developer or your “work”? (4) Can you run it in a VM? – Scott – 2018-03-02T17:04:45.743
@Scott: (1) it was a mistake, I corrected my question (before your edit but after JakeGould's quote), I am using the game for gaming, but I also do personal work on the same computer. – Anne Aunyme – 2018-03-02T17:17:24.083
@Scott: (2) can you detail what changes between the two modes? It would make a perfectly valid answer. I don't need you to decide for me, just to explain me how things work. (3) no, tech support don't want to explain me anything (4) I haven't tried. I can run it the normal way, with normal privileges, and it kinda work except it is buggy. – Anne Aunyme – 2018-03-03T17:22:44.447