The best approach here is to use cat along with a comma-separted list created by {} indexing to yield the expected column vector. We specify the first dimension as the first argument since you have all column vectors and we want the output to also be a column vector.
out = cat(1, extInt{vec})
Given your input, cell2mat attempts to concatenate along the second dimension which will fail for your data since all of the data have different number of rows. This is why (in your example) you had to transpose the data prior to calling cell2mat.
Update
Here is a benchmark to compare execution times between the cat and cell2mat approaches.
function benchit()
nRows = linspace(10, 1000, 100);
[times1, times2] = deal(zeros(size(nRows)));
for k = 1:numel(nRows)
rows = nRows(k);
data = arrayfun(@(x)rand(randi([10, 50], 1), 1), 1:rows, 'uni', 0);
vec = 1:2:numel(data);
times1(k) = timeit(@()cat_method(data, vec));
data = arrayfun(@(x)rand(randi([10, 50], 1), 1), 1:rows, 'uni', 0);
vec = 1:2:numel(data);
times2(k) = timeit(@()cell2mat_method(data, vec));
end
figure
hplot(1) = plot(nRows, times1 * 1000, 'DisplayName', 'cat');
hold on
hplot(2) = plot(nRows, times2 * 1000, 'DisplayName', 'cell2mat');
ylabel('Execution Times (ms)')
xlabel('# of Cell Array Elements')
legend(hplot)
end
function out = cat_method(data, vec)
out = cat(1, data{vec});
end
function out = cell2mat_method(data, vec)
out = cell2mat(data(vec)');
end

The reason for the constant offset between the two is that cell2mat calls cat internally but adds some additional logic on top of it. If you just use cat directly, you circumvent that additional overhead.
cellfun