Has anyone encountered a scenario, where one single device (desktop) is reported to have accounted for thousands of Unique Visitors, reported for a single page, in a day? What this device could be? And what is it doing?
You may have someone trying performance/penetration testing on a given page.
Check with your IT dept.
Also check with Marketing teams could be related to an ad buy as some marketing companies buy/sell traffic that is funnelled via a common gateway or used to artificially increase apparent banner traffic.
If not an internal performance/pentetration test from your IT Dept, depending on the page (i.e. content on that page) it could also be a bot trying to scrape content (this is common on media sites as there are a lot of bots trying to scrape content to post to things like aggregators).
Bots wouldn't necessarily allow cookies to be written which is why each time it hits the page it's treated like a new visitor... Or it could be a more malicious type bot trying to find vulnerabilities to exploit them or trying to create a DDOS attack.
If it's a malicious behaviour, you may need to check with your IT team to block traffic to the site based on behaviour such as coming from the same IP address and making more than X requests over a specified period of time (this should be easy to create if your site is using a cloud service like Cloudfront or CloudFlare, etc.