You have a gaps and islands problem here, you could use the difference between two row_numbers approach to create groups :

with cte as (
  select *, row_number() over (order by store_id) 
          - row_number() over (partition by city_id, store_type order by store_id) as grp
  from store
)
SELECT MIN(store_id) AS min_store_id,
       MAX(store_id) AS max_store_id,
       max(city_id) as city_id,
       max(store_type) as store_type
FROM cte
group by grp

Result :

min_store_id    max_store_id    city_id store_type
1               50              1       regular
51              70              1       express
71              90              2       regular
91              105             1       regular

Demo here

The other answer is much cleaner, but since I put in the time I'm posting anyway.

As already stated its a gaps-and-islands problem, you need a way to mark each group you want to analyse.

Explanation in the SQL.

create table Test (store_id int, city_id int, store_type varchar(12));

insert into Test (store_id, city_id, store_type)
values
(1,     1,  'regular'),
(2,     1,  'regular'),
(3,     1,  'regular'),
(50,    1,  'regular'),
(51,    1,  'express'),
(55,    1,  'express'),
(58,    1,  'express'),
(70,    1,  'express'),
(71,    2,  'regular'),
(75,    2,  'regular'),
(78,    2,  'regular'),
(80,    2,  'regular'),
(85,    2,  'regular'),
(90,    2,  'regular'),
(91,    1,  'regular'),
(95,    1,  'regular'),
(97,    1,  'regular'),
(100,   1,  'regular'),
(105,   1,  'regular');

with cte1 as (
select *
  -- If the store_type or the city_id changes its a new group[
  , case when store_type <> lag(store_type, 1, store_type) over (order by store_id)
  or city_id <> lag(city_id, 1, city_id) over (order by store_id) then 1 else 0 end Transition
from Test
), cte2 as (
  select *
    -- Sum the transitions to provide a unique group id
    , sum(Transition) over (order by store_id) [Grouping]
  from cte1
)
select
  -- Calculate desired results per group
  min(store_id) min_store_id
  , max(store_id) max_store_id
  , city_id
  , store_type
from cte2
group by
  city_id
  , store_type
  , [Grouping]
order by min_store_id;

Returns

Note: Providing the DDL+DML as shown here makes it much easier for people to answer.

db<>fiddle