Source: I'm a vegetarian, and I pay scrupulous attention to this stuff.
From Google, 1 ounce of Chia seeds is 4.7 gms of protein, 138 calories. I would have to eat 31 ounces of Chia seeds to get 150 gms of protein. That is 4030 calories per day. Guess what happens then? I gain weight.
Quinoa provides 3.8 grams of protein per 100kcal of energy [1]. Boneless skinless chicken breast provides 18.8 grams of protein per 100kcal of energy [2].
A weightlifter who wished to consume 100 grams of protein per day would have to eat 2632 kcal of quinoa, vs. 532 kcal of chicken breast.
Just as a quick look to see details as to what would be required. Quinoa is hardly the only source of non-meat protein.
Now, yes that does include a lot of protein shake stuff, that's not that unusual for most weightlifting diets. That's also a vegan diet, so you might be able to add eggs, cheese and milk to that diet and cut back on the powder in the meals if you just wanted to be vegetarian.
The powder is of course to solve the issue you pointed out already.
I'm not vegan, so I've never bothered trying them, but it doesn't seem like it'd be a big problem.
My concern (see my other comment) would be that the diet shown certainly is extremely high calorie, and it looks like it'd be pretty much all nasty shakes to get it down to a more normal level with the same amount of protein.
(EDIT: Note, this would only really be an issue if you do heavy resistance training, as the protein level in that diet is very high for someone who isn't doing weight lifting)
For comparison, I'm a powerlifter. I'm 238lbs currently. My maintenance calorie intake is roughly 2450kcal on average. I aim for about 2800kcal on training days, and equivalently lower on rest days to roughly meet that average. Fitting 220g or so of protein in that is not that hard: I can eat 400g lean chicken and get 100g protein for <900kcal. I can tack on 100g beef jerky and get another 50g protein for less than <300kcal; which leaves it almost hard not to meet the protein target within my calorie goals.
If I were to eat 3387kcal to meet 207g protein, I'd be adding 1-2kg a week.
That's well in excess of the protein synthesis a typical human male body is capable of. In other words: A substantial percentage would be fat. Quite possibly I might end up adding 1.5kg of fat a week on a diet like that, which would get me quite a lot less protein than what I do on my current diet.
For a body builder exercising heavily 2-3 hours a day, on steroids (otherwise lifting heavily for that long every day would just be a total waste of time), that calorie intake might be reasonable. Or for someone who combines the exercise with a highly active job, like say, construction.
It'd be interesting to see that diet brought down to 2400kcal or below with the same protein levels. I suspect it would look a whole lot less pleasant (and that diet looks awful to me in the first place, but I love my meat).
(Now, protein amounts this high are in the "might as well, just in case" level - the possible incremental benefits hinted at in the literature are as far as I know quite marginal - so a lower protein intake would not necessarily be bad, and then it'd quickly become a lot easier to meet it with a reasonable calorie intake)
https://drive.google.com/file/d/0B4anS4KxXuQdUlo3NEtUZ0xROFU...
We're not going to "solve" the problem until we have a ton more data (maybe sensors in everyone along with the understanding of the markers to look for) so we can fit you to an optimal path based on a lot of observed variables. But even then we're just going to be playing percentages off each other, and contrary to the life-extender crowd out there, it may turn out that there is no 110-year optimal path for most of us, at least until we start reengineering the body at a more fundamental level.
You can get enough protein for weight training on a vegetarian diet btw.