Wolves tend to be surprisingly big, and come close to human size, so an extension of that to tiger size isn't too much of a stretch.
The Wikipedia article on them cites Bergmann's Rule might be in play when it comes to wolf size, with wolves in colder climates being larger than their counterparts in warmer climates.
Their size could be explained either by evolutionary fluke, or that they come from a cold climate, and possible the equivalent of the artic/antarctic (lycic/antlycic?). The poles tend to be extremely cold, and flat, which helps minimise the downsides of being large (not having to get around a complex terrain like a jungle), and means that they get a benefit from the larger size (more thermal mass).
They are among the few animals that are not afraid to humans, and that are not dangerous from humans neither (like capybaras, and emperor penguins);
They could be relatively friendly to humans because they're unfamiliar with them, and humans don't resemble their prey, but it might be paradoxical to make them not dangerous.
Even if it isn't actively trying to attack you, a large animal like that is inherently dangerous. What it might consider perfectly innocent could easily endanger a human, like lying down on top of one, or play-fighting.
They have a great hair colour diversity: 60% of them have red fur, 20% of them have black fur, 10% of them have white fur, 6% of them have blonde fur, and 4% of them have grey fur;
This does conflict with the polar wolf idea a bit, since red fur wouldn't really work for the arctic, or at least an Earth equivalent.
Some form of desert might make sense, since adaptations to red sand may result in red fur.
But then you have issues with other fur colours, which aren't well optimised for that environment, unless they're mutant variations.
Most have a fur as dense as a long-furred chihuahua, but some have a fur as dense as a pug;
Again, this also runs into problems with it being difficult to match up with the other conditions. Humans were only able to get that variation in dogs through temperate climates and selective breeding.
Evolutionary pressures with the same result may not be compatible with the kind of climate that would create that big of an animal as you want in Point 1, or the evolutionary pressures that result in Point 2.
Especially since neither of those breeds of dog have a particularly thick coat that would be useful in the kinds of cold climate that might help them evolve to be as large as tigers.
They tend to be solitary, or at most, they live in quintets (group composed from five individuals), and most of them are monogamous or bigamous;
This would make sense if they lived a highly competitive environment, where there is neither the predation pressure, nor the resources to sustain a particularly large group, like polar bears.
The place of Earth that can be considered their cradle is Northern Quebec, Canada, Western World, and they can naturally be found in any parts of North America, and Eurasia that are not tropical;
Although those are all temperate zones, which would lend themselves to smaller animals like mice, or wombats. A tiger-sized red wolf is going to stand out quite a bit on a green and grassy field.
If the grass was red, maybe, but in temperate zones, the large size is going to be more of a disadvantage compared to a smaller one, even excluding the possibility of them being hunted to extinction by early homonids, precisely because they aren't actively hostile towards humans. It basically happened to the Great Auk, where their friendly disposition towards humans made them easy hunting. The large size of canis major (BigDog) would only make them bigger and more tempting targets.
They have a domesticated form that is the most popular pet among giant humans (Homo gigas);
"Domesticated" is doing quite a lot of work here. Are they domesticated like early wolves were, becoming dogs?
But all you really need for domestication to occur is for both species to decide that they worked better together instead of apart, and they will domesticate each other given enough time.
Humans did evolve the ability to read dog emotions from their faces, and dogs have famously done the same with human emotions.
They can breed with domestic dogs, grey wolves, and even coyotes, and the resulting offspring tend to be fertile (like a coywolf, a coydog, or a wolfdog).
The mechanics of this might be rather difficult. BigDogs are still tiger-size, which may cause problems with breeding, even if they have compatible genetics.
Especially if BigDog mating behaviour is similar to that of regular dogs, which would make it dangerous for a regular-sized dog. (Biting and all of that may lead to a grisly end).
You might be able to sidestep some of those issues with BigDogs having evolved from wolves that ended up migrating to the polar regions, which might help with genetic compatibility, but then you run into problems with the evolutionary pressures not being right for either their large size, fur colour, or behavioural characteristics.
Wild Wolves aren't exactly friendly to humans.