Debatable. DotA 2 yields around $100m revenue annually, a quarter of which goes to funding tournament prize pools. From the remainder, they have tournament organising costs, developer salaries, server costs and so on. I’m sure it’s profitable at the end of the day, just not the main source of their profit.
A bigger source of their profit is taking 30% of most PC gaming revenue with minimal overhead. This was such a money spinner that other game publishers eventually got wise to it and started their own stores. But Steam is still the big dog here.
Whilst it is somewhat difficult to find up to date information, it looks like DotA 2 yields somewhere north [1] of $18M/month [0] in revenue, which is more than double the number you've referenced here.
Not to suggest that a good slice of Valve's profits don't come from Steam, but they still make a reasonable amount from individual games.
Every TI, the prize pool surpasses 25m. Which means that just by buying compendiums and treasures, people have already paid 100m (25% is contributed towards the prize pool).
There's also multiple compendiums per year, or battle passes or whatever depending on the year.
And there's a lot of random loot box releases, Arcana items etc.
On top of that, Valve extracts an extra 10% (or is it 15%) of the trade value of every item that gets sold through the steam market. And those items are sold and bought A LOT.
A bigger source of their profit is taking 30% of most PC gaming revenue with minimal overhead. This was such a money spinner that other game publishers eventually got wise to it and started their own stores. But Steam is still the big dog here.