He is just sharing what worked for him. Any diet where you consume fewer calories will allow you to lose weight, it is just a question of choosing one you will stick with.
You absolutely don't need to do the paleo/keto nonsense at all. I eat meat twice a week and barely eat any dairy (just a little cheese once in a while). I eat pasta, white rice and potatoes all the time. I've lost 68 pounds so far as of this morning. No matter how much people want to pretend there is magic involved, or point to hilariously bad books like Taubes' junk, it really does come down to "burn more calories than you consume".
I can't tolerate low carb diets, I feel hungry and tired all the time and end up going nuts after a couple weeks and breaking down and eating a ton of pasta. So I didn't go low-fat or low-carb, I just eat reasonable portions, make sure the food I eat is always satisfying, and exercise. I find it much easier for me to increase the calories I am burning than to decrease the calories I am consuming too far.
And contrary to what spking says, it is not hard at all to get enough protein as a vegetarian. You only need ~55g a day, which I get easily on days where I don't eat meat. On meat days I end up around 90g. If you are doing heavy lifting you'll need maybe 20g a day more than average, and if you do endurance sports you could need up to double the average. But if you aren't doing either of those things, you should easily get enough protein without making any special effort or using supplements.