I don't believe that Shostakovich was thinking of Beethoven here. Of course he knew the 7th Symphony.
If anybody could answer this would be Gerard Schwarz. But he mentions the name of Beethoven only in another context. (2:06)
If you want to find an other similarity to Beethoven's 7th there is one in the accompaniment at 13:45, but this would be very, very searched.
I've copied here the whole subtitles:
(1:58) I think it's important to know that by the time we're here in 1937, composers were much freer about form. So, where Beethoven or Schuman pretty muchworked in the first movement
in what we call sonata form
where you have the exposition
where all the material is exposed,
the development, all that material is developed,
and the recapitulation,
where all that material is reprised;
a composer like Shostakovich,
yes, they did some of that,
and sometimes they did it absolutely
in an old fashioned way.
Other times, it was very free form.
This symphony's first movement,
even though it feels very organic,
it feels like it belongs the way it's written,
is very much in the style
of being free form.
It begins in an interesting way.
("Symphony No. 5" by Dmitri Shostakovich)
(3:07) It's an introduction,
but it's an aggressive introduction,
and it's a canon.
It starts with the cellos and the basses.
They play this [gentle instrumental music],
and then the violins play [gentle instrumental music],
and then the cellos and basses [gentle instrumental music],
and the violins [gentle instrumental music].
And then that canonic gesture carries on now.