I agree.I will first check where I am getting most traffic from and what people are checking my site, then I will use a method to reach that demography and geo-location. It is very important to check your stat before promotion.

I think that's a must have feature for pet sites, alot of members will share links on social media, especially if there's good incentives to get referrals.I agree.
A referral system can be a good strategy for this. Allowing users to earn in-game points, items or other rewards for referring new players can help you promote your site cost-effectively.
Word-of-mouth growth is often much more powerful than paid advertising. In fact, I’ve noticed that only a few pet sites have launched paid advertising campaigns, while others have grown primarily through word of mouth.
The /virtualpets subreddit is a restricted community and hasn’t seen any activity for almost a year. However, the virtualpetgaming subreddit isn’t restricted and would be a good place to promote.The social networks such as Twitter or Instagram and web communities including Reddit /r/virtualpets are good platforms to use. You can also join online pet forums like virtualpetlist.
With Instagram enabling links on pictures, I'd say it's a good way to promote. Making videos on Tiktok can also help as they've also enabled links to be included on videos that are uploaded on their platform as well.One can successfully promote virtual pet site through social media platforms like Twitter and Instagram, gaming forums And then we can go on online directories and listings meant for virtual pet sites.